Education:

University of Michigan, BGS, 1973

University of Washington, MS Physics, 1978

The Rockefeller University, PhD Physics, 1982

Experience:

Los Alamos National Laboratory, Postdoctoral Research Associate, 1982-1984

Argonne National Laboratory, Postdoctoral Research Associate, 1984-1987

State University of New York at Fredonia, 1987-2018, Physics Department Chair 2001-2013

Selected Publications:

(most available electronically from Physics Preprint Archive, http://arxiv.org)

• • "Possible new phase transition in the 3D Ising model associated with boundary percolation," J. Phys. Condens. Matter 35 (2023) 285401 arXiv:2301.08424[cond-mat] (note: arXiv version slightly older)

  • "Exploring the 3D Ising gauge-Higgs theory in exact Coulomb gauge and with  a gauge-invariant substitute for Landau gauge," arXiv:2109.04560[hep-lat]

  • "Two time solution to quantum measurement paradoxes," quant-ph/708.04275 (2017).

  • "Solution to the gauge-Higgs analyticity paradox," hep-lat/1502.04362 (2015).

  • "Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory," hep-lat/1306.6921, Nucl. Phys. B 876 (2013) 794-809. 

  • "Toward a proof of long range order in 4-d SU(N) lattice gauge theory," hep-lat/1210.1794, Mod. Phys. Lett. A, Vol. 28, No. 19 (2013) 1350087. 

  • "Connecting phase transitions between the 3-d O(4) Heisenberg model and 4-d SU(2) lattice gauge theory," hep-lat/1104.3331  (2011)

  • "Reconsidering gauge-Higgs continuity", hep-lat/0507037, Physics Letters B, 626, 161 (2005).

  • "Critical or tricritical point in mixed-action SU(2) lattice gauge theory?", hep-lat/0404015, Nuclear physics B, 713, 204 (2005).

  • "Quantum Mechanics, Quantum Gravity, and Approximate Lorentz Invariance from a Classical Phase-Boundary Universe", hep-th/0104237 (Ch. 3 in "Trends in Quantum Gravity Research," NOVA Science Publishers, 2006).

  • "Gauge Invariant SO(3)-Z2 Monopole as Possible Source of Confinement in SU(2) Lattice Gauge Theory" hep-lat/9806024.

  • "Universe as a Phase Boundary in a Four-Dimensional Euclidean Space", gr-qc/9805076.

  • "Monopole Loop Distribution and Confinement in SU(2) Lattice Gauge Theory", hep-lat/9802035, Physics Letters B, 455, 239 (1999).

  • "Monopole Loop Suppression and Loss of Confinement in Restricted-Action SU(2) Lattice Gauge Theory", hep-lat/9801016.

  • "Deconfinement from Action Restriction", hep-lat/9609004, Nuclear Physics B (Proc. Suppl.) 53, 599 (1997) (LATTICE 96).

  • "Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement," hep-th/9409049 (1994).

  • "Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with Extended Action" (with Rajiv Gavai and Manu Mathur) hep-lat/9403001 Nuclear Physics B 423, 123 (1994).

  • "Can a Logarithmically Running Coupling Mimic a String Tension?", Physical Review D 50, 6009 (1994).

  • "Cabibbo Mixing from Strong-interaction Condensates", Nuovo Cimento 105A, 1065 (1992).

  • "Spurious First-Order Phase Transitions from Topological Effects on the Lattice", Nuclear Physics B 365, 699 (1991).

  • "Hadron Spectra and Potential Screening for Lattice QCD  with Dynamical Quarks" (with D.K. Sinclair and J.B. Kogut), Phys. Lett. B 200, 149 (1988).

  • "Alternative Scaling Hypothesis for SU(2) and SU(3) lattice gauge theories," Z. Phys. C - Particles and Fields, 39, 125 (1988).

  • "Numerical Study of the Lattice Massive Schwinger Model using a Fast Fermion Monte-Carlo Algorithm," Phys. Rev. D 35 1961 (1987).

  • "Fast Algorithm for Monte Carlo Simulations of Systems with Fermions," Phys. Rev. D 32, 1496 (1985).

  • "Obtaining Mw=MzCos theta in Technicolor Theories," Nucl. Phys. B 221, 16 (1983).

  • "Conserved Charges from Self-Duality" (with Louise Dolan), Phys. Rev. D 25, 1587 (1982).

  • "An Infinite Set of Conserved Charges in the Ising Model," Phys. Rev. D 25, 1103 (1981).

A Guide to my Research

My research for the most part follows certain themes that can be organized under hypotheses.  Many of these are somewhat or wholly heretical toward consensus theories.  I did not really set out to be a heretic, but as I followed what seems to me as logical progressions, this is where I have ended up. In my opinion science flourishes when all ideas are given some consideration, rejecting only  those that are clearly provably wrong.  After all, there are hundreds of examples where consensus theories have eventually been proven wrong, and replaced by others which were initially considered heretical.  Suppressing ideas that challenge the status quo, as happened for decades in the Soviet Union in the field of biology, for example, can have disastrous consequences,

Probably my somewhat different conclusions result partly to my having worked much of my career in relative isolation, at the State University of New York at Fredonia,  a relatively small and isolated primarily undergraduate college in rural Western New York.  Although I regularly attended meetings, I spent a lot of time in solitary thought that evolved in its own direction.   Many of the avenues I pursued could only be accomplished using new techniques and algorithms I have developed.  Unfortunately, that has made my results a bit harder for others to judge, because the techniques are unfamiliar.

• • "An Infinite Set of Conserved Charges in the Ising Model," Phys. Rev. D 25, 1103 (1981).

  • "Conserved Charges from Self-Duality" (with Louise Dolan), Phys. Rev. D 25, 1587 (1982).

• • "Obtaining Mw=MzCos theta in Technicolor Theories," Nucl. Phys. B 221, 16 (1983).

  • "Cabibbo Mixing from Strong-interaction Condensates", Nuovo Cimento 105A, 1065 (1992).

• • "Fast Algorithm for Monte Carlo Simulations of Systems with Fermions," Phys. Rev. D 32, 1496 (1985).

• • "Numerical Study of the Lattice Massive Schwinger Model using a Fast Fermion Monte-Carlo Algorithm," Phys. Rev. D 35 1961 (1987).

The largest part of my work has been in this area.  All lattice gauge theories confine at strong coupling. This is due to the compactness of the action.  When the inverse coupling β goes to zero,  the Boltzmann weight for all configurations becomes almost equal, leading to total randomness.  Random configurations are confining.  Abelian lattice gauge theories in four dimensions, such as U(1) (electromagnetism), undergo a phase transition to a deconfining phase as β is raised, resulting in a deconfined continuum limit (β  →  ∞ ).  So, electromagnetism doesn't confine.  The strong coupling phase of U(1) lattice gauge theory does confine, but it has nothing to do with the continuum theory, since they are separated by a phase transition.  It can be shown that confinement in U(1) lattice gauge theory is due to the proliferation of U(1) monopoles, a lattice artifact that ceases to exist in the continuum limit. In the early days of lattice gauge theory it was noticed that non-abelian theories such as SU(2) and SU(3) did not have a noticeable phase transition. It was hypothesized that these have only a single confining phase, which would be consistent with the apparent confinement of quarks seen in the physical strong-interaction case (mesons and baryons) described by the theory of Quantum Chromodynamics (QCD) which is based on an SU(3) gauge theory, describing the gluon degrees of freedom, and quark fields.  The "pure" SU(3) lattice gauge theory alluded to above does not have light quarks, so it is not the full theory of QCD, although nowadays lattice gauge theories are studied with dynamical quarks included.  If the hypothesis of no phase transition for the non-abelian lattice gauge theories is correct, then that would mean that the gluons themselves are responsible for confinement, and one does not need light quarks in the theory to see it.

Around 1983 I saw a presentation by Dan Caldi where he asked whether one could really tell the difference between the U(1) and SU(2) theories as far as a phase transition was concerned, given the data available.  I think he concluded that you could, but the data for SU(2) could not completely rule out the scaling that would be associated with  a phase transition at a finite β,  similar to that in U(1).  This led me to peruse this question further.  Certainly it would be convenient  if there were no phase transition for SU(2) and SU(3), as that provides a nice explanation for confinement, but what if it wasn't true?  Maybe confinement has a different cause.  After all V.N. Gribov has argued that confinement is due to the light quarks in a mechanism similar to sparking the vacuum by an electrically charged nucleus exceeding 137.  If this were true, then the theory with only gluons would presumably not confine.

The widely accepted hypothesis that the non-abelian theories have no phase transition is actually quite radical from the point of view of lattice spin models, which have a lot of similarities to gauge theories.  Lattice spin theories such as the Ising model or Heisenberg model are models for magnets.  They have a global symmetry that is unbroken in the high-temperature random phase and spontaneously broken in the low temperature phase.  These all have phase transitions (given enough dimensions) regardless of whether they are abelian or non-abelian.  At zero temperature the spins are aligned in a perfectly ordered magnetic phase and at infinite temperature that are completely disordered, with no magnetism present.  Indeed all physical magnets also behave in this way.  Lattice gauge theories differ from spin theories in that the symmetry is now a local one, which cannot break spontaneously due to Elitzur's theorem.  Because of this, some would say they are very different from spin theories.  Nevertheless, some LGT's such as U(1) and Z(2) still undergo phase transitions from a random (confining) phase to a more ordered phase at weak coupling  (strong coupling in the gauge theories corresponds to high temperature in the spin theories).  If one fixes to the Coulomb gauge, then the local symmetry is removed, and replaced by a remnant symmetry which is global in three dimensions and still local in one, a kind of layered global symmetry.  In this gauge, the LGT looks much more like a spin model, in that it has a global symmetry that can break spontaneously.  In fact, in theories such as Z2 (gauged Ising model) the  Coulomb remnant symmetry does break spontaneously at the known deconfining phase transition, and confinement-deconfinement can be associated with this magnetic phase transition with a local order parameter.  It has been proven by Zwanziger and others that a phase with unbroken remnant symmetry in Coulomb gauge is necessarily deconfined.  Because of this connection of LGT's to magnets when in the Coulomb gauge, it is very hard to imagine how the non-abelian theories could avoid having an ordered phase  at weak coupling, as all other magnetic theories do.  Incidentally, there is nothing wrong with gauge-fixing in lattice gauge theory.  In the continuum theory, one always fixes the gauge for computations, and all gauges should give identical results for gauge-invariant quantities.

There is one case in which a spin and a gauge theory are completely equivalent.  The Z(2)  lattice gauge theory in three dimensions is dual to the three dimensional Ising model.  Theories which are dual have identical partition functions and are essentially equivalent.  However one of these is a gauge theory with only a local symmetry and the other is a spin theory with a global symmetry that breaks spontaneously.  Duality implies that they both have essentially identical phase transitions.  So one cannot say that gauge theories and spin theories are always fundamentally different.  This example shows that the local symmetry of the gauge theory can hide the true symmetry-breaking nature of the phase transition, however, which can be revealed using Coulomb gauge fixing.  There are some people that say that phase transitions in lattice gauge theories are never symmetry breaking, due to Elitzur's theorem, but this example shows that to be false through the duality connection.

My first paper suggesting a zero-Temperature phase transition to a non-confining phase at finite beta was 

• • "Alternative Scaling Hypothesis for SU(2) and SU(3) lattice gauge theories," Z. Phys. C - Particles and Fields, 39, 125 (1988).

In this paper, I showed that quantities such as the string tension could be fit to the scaling law that would be associated with such a phase transition, with a critical beta around 2.8.   The  data quality and lattice sizes from that era computers were low by today's standards.  Although I believe this paper is more or less correct, I now believe beta-c is quite a bit higher, around beta=3.2, and the critical exponents found in this paper are quite off.   I also introduced the idea of physical confinement arising from the chiral condensate.  The chiral condensate is made of zero-momentum bound pairs of mostly u and d quarks bound to their antiparticles that fill the strong vacuum.  These bound pairs are bosons which can multiply occupy their ground state.  It has been shown that strong color fields disrupt and diminish the chiral vacuum.  So if  one tries to pull a quark away from its partners in a meson or baryon, the color field exposed will push away the chiral condensate, which will push back, giving a bag-like pressure which could simulate confinement.  

Probably the best way to look for a zero-temperature deconfining phase transition is to fix to Coulomb gauge, and look for the remnant symmetry breaking.  This is a local order-parameter for confinement (as apposed to say the Polyakov Loop which is a global parameter).  Unfortunately it is rather hard to set Coulomb gauge which is usually done with an overrelaxation procedure.  Sometimes it gets hung up on a local minimum.  Often "best of 10" minimizations is used, however there is still a hard to control systematic error present from imperfect gauge-fixing.  I have found that most of the difficulties of Coulomb gauge fixing can be removed by using open boundary conditions.  This results in hundreds of times less variance between different  minimizations. Open boundary conditions cause some headaches, but are workable if one uses large lattices and stays some distance from the boundary.  A detailed study of Wilson-action SU(2) lattice gauge theory in the Coulomb gauge is given in 

• • "Connecting phase transitions between the 3-d O(4) Heisenberg model and 4-d SU(2) lattice gauge theory," hep-lat/1104.3331  (2011)

It is in the second half of this paper, which is on a somewhat different topic.  In hindsight these should have been two separate papers.  Here I find, using standard techniques such as Binder cumulant crossings and scaling collapse plots, that there is indeed an infinite-lattice phase transition at beta = 3.18(8) with critical exponent nu=1.71.  It is also shown that string tensions measured on various lattice sizes scale to this finite-order scaling law, with the same critical point, at which the string tension vanishes.  Incidentally, extraction string tensions from the interquark potential is quite tricky, because  the coulomb term should really have a running coupling. This is explored in another of my papers:

• • "Can a Logarithmically Running Coupling Mimic a String Tension?", Physical Review D 50, 6009 (1994).

Although the Coulomb gauge result seems definitive, I have taken two other approaches to the subject to prove that SU(2) lattice gauge theory has a zero-temperature phase transition at finite beta, and does not confine in the continuum limit.  One of these is to consider extended coupling spaces in which there is a well-recognized symmetry-breaking  phase transition, and show that it connects to the SU(2) LGT.   There are several ways to do this.

Another approach is to try to find the lattice artifacts which are responsible for confinement and suppress those in the action.  This gives models with the same continuum limit as standard SU(2) lattice gauge theory, but in which there is no confinement at all, even in the strong-coupling limit.  I have been quite successful with both of these approaches.

The first paper showing a connection from SU2) lattice gauge theory to a known phase transition was:

• • "Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with Extended Action" (with Rajiv Gavai and Manu Mathur) hep-lat/9403001 Nuclear Physics B 423, 123 (1994).

This paper looked at the finite-temperature phase transition of the Polyakov Loop, and followed that into an extended action plane,  the fundamental-adjoint plane.  Here an adjoint term is added to the action, in addition to the usual fundamental term.  It is well known that a bulk fist order phase transition exists in this model, some distance away from the fundamental axis.   We found that the finite temperature transition appeared to join with the bulk transition at its endpoint.  If they really join, then both transitions have to be bulk (zero-temperature).  In my interpretation, what is usually considered a finite-temperature transition is simply the zero-temperature transition shifted in coupling by the truncated lattice.  However, others argued that perhaps the finite-temperature transition did not really join the bulk phase transition, but merely ran very closely alongside it.  This question is not easily resolved with numerical data, so I sought other arguments and connections.   Staying first with the fundamental-adjoint plane,  I  took a closer look at the bulk transition itself.  First-order transitions come in two different flavors, symmetry-breaking and non-symmetry breaking.  For instance, the liquid-gas transition for something like water is non-symmetry breaking.  It ends at a critical point beyond which there is no distinction between liquid and gas, because the gas is so compressed it looks the same as a liquid.  There is no symmetry distinction between gas and liquid - they are both amorphous states.   The non-symmetry breaking first-order transition is characterized by a Landau free-energy which is a cubic function.  A first-order transition can also be symmetry-breaking.  This is characterized by a sixth-order landau free energy, with a negative fourth-order term.   As the second-order term is adjusted, the minimum energy can suddenly jump from the zero-field value to a finite non-zero value, inducing a first-order phase transition.  I discovered in the paper

• • "Critical or tricritical point in mixed-action SU(2) lattice gauge theory?", hep-lat/0404015, Nuclear physics B, 713, 204 (2005).

that one could tell these two kinds of first-order transitions apart by examining the scaling of the size of the metastable coupling region with latent heat. In one case it is linear and the other quadratic.  These are easy to distinguish, and the fundamental-adjoint SU2) theory definitely came out as symmetry-breaking according to this test.  However, a symmetry-breaking phase transition cannot end at a critical point like the liquid-gas case.  Instead, the first order phase transition can turn into a second order one at a tri-critical point, when the fourth-order term in the landau free energy changes from negatives to positive.  This second order transition is pointing in a direction that will take it across the fundamental axis, giving the SU(2) lattice gauge theory a zero-temperature phase transition there.  The reason this phase transition was not seen in the early days of lattice gauge theory is that it is a weak second-order transition with a negative specific-heat critical exponent alpha. This means that the specific-heat does not have an infinite singularity at the critical point - only the second and higher derivatives do.   For this reason, looking only at the energy quantities, the phase transition is difficult to detect.  The poof that a symmetry-breaking phase transition  exists anywhere in an extended coupling plane is powerful, because symmetry-breaking phase transitions can only end at the edges of the phase diagram.  In my opinion this paper proves my hypothesis of a zero-temperature deconfining phase transition in SU2) lattice gage theory.

There is another extended coupling plane where similar arguments can be made. This is by allowing a different coupling constant for space-space (horizontal) plaquettes and space-time (vertical) plaquettes.  When the inverse-coupling for vertical plaquettes is set to zero, the model becomes a set of 3D O(4) spin models which has a symmetry-breaking magnetization phase transition.  This extended-coupling is treated in:

• • "Connecting phase transitions between the 3-d O(4) Heisenberg model and 4-d SU(2) lattice gauge theory," hep-lat/1104.3331  (2011)

in the follow-up paper to this ,

• • "Toward a proof of long range order in 4-d SU(N) lattice gauge theory," hep-lat/1210.1794, Mod. Phys. Lett. A, Vol. 28, No. 19 (2013) 1350087. 

I showed that this magnetic phase transition had to enter the phase diagram.  Once entered, it had to continue to another edge, unavoidably crossing the line of equal horizontal ad vertical couplings (ordinary SU(2) lattice gauge theory.   This again proves the existence of such a phase transition.

A final approach I took to the phase transition question in SU(2) was to search for lattice artifacts that may be causing confinement, similar to the way that U(1) monopoles and vortices cause confinement in that theory.  For U(1), if the artifacts are eliminated then the theory remains unconfined for all couplings.  SU(2) plaquettes can be decomposed into a Z2 factor and an SO(3) factor.  Since Z2 strings are responsible for confinement in Z2 lattice gauge theory, I first tried eliminating plaquettes with a non-trivial Z2 factor (i.e. -1) using a positive-plaquette restriction in the action.  This is perfectly acceptable because in the continuum limit only plaquettes near unity survive.  The positive-plaquette action weakened confinement but did not remove it completely.  I then began looking into the non-abelian Bianchi identity, which is a statement of flux conservation.  It states that the product of the six untraced plaquettes bounding a unit cube is unity (the plaquettes have to have tails added so they all start at the same point).  One can also think of this as the product of three L-shaped double plaquettes.  These double-plaquettes can also be factored into  Z2 and an SO(3) parts.  The identity can be solved if the three Z2 factors multiply to unity, as do the three SO(3) factors, or conversely these factors can both be -1.  If the latter is the case I call this object an SO(3)-Z2 monopole, because a nontrivial Z2 flux is cancelled by a non-trivial SO(3) flux.  These objects are gauge invariant and  do not exist in the continuum limit, so are lattice artifacts.  Because they look like SO(3) charges, they could introduce the randomness needed by confinement.  The monopoles are introduced in 

• • "Gauge Invariant SO(3)-Z2 Monopole as Possible Source of Confinement in SU(2) Lattice Gauge Theory" hep-lat/9806024.

and their elimination (together with z2 strings) was shown to lead to a theory that was non-confining at all couplings:

• • "Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory," hep-lat/1306.6921, Nucl. Phys. B 876 (2013) 794-809. 

The potential for this model is consistent with a Coulomb potential with a logarithmically running coupling.  In Coulomb gauge the theory remains in the symmetry-broken (non-confining) phase, even in the strong-coupling limit.   Although eliminating these artifacts directly in the action is the "gentlest" way to get a non-confining theory, one can also restrict the plaquette to a value larger than 0.707, which would not allow even double-plaquettes to be negative.  This  restriction also kills confinement, but has the disadvantage of  a smaller physical lattice spacing, requiring larger lattice sizes.  This approach was shown in an earlier paper:

• • "Deconfinement from Action Restriction", hep-lat/9609004, Nuclear Physics B (Proc. Suppl.) 53, 599 (1997) (LATTICE 96).

Other researchers have shown that one can attribute confinement to abelian monopoles seen in non-abelian theories in the "maximal abelian gauge."  I looked at the distribution of large monoploe loops as a function of coupling and showed that large enough loops to cause confinement do not survive the continuum limit, even in the Wilson-action case:

• • "Monopole Loop Distribution and Confinement in SU(2) Lattice Gauge Theory", hep-lat/9802035, Physics Letters B, 455, 239 (1999).

This is consistent with my observation of a deconfining zero-temperature phase transition at an inverse coupling, beta, of around 3.2. 

Phase Boundary Universe

In 1994 I began thinking about a new cosmological model, an expanding 3d sphere in a 4-d Euclidean space.   This is a toy model that is often used to help people picture a closed expanding universe, but  I thought it could be made into a serious contender. What I think is an original idea, is that this surface is conjectured to be  a phase boundary between two phases, pictured as a liquid becoming a solid crystal. I picture that there is also a time dimension, which could even be an absolute Newtonian time.  The surface of the growing crystal is where we are - and what we define as the "present."  Matter exists as surface modes on this boundary, which extend into the past, which is the frozen crystal.  The universe evolves as the crystal grows into the relatively undifferentiated random liquid, thus becoming our future.  This idea was first introduced in an essay that was submitted to the annual contest of the Gravity Research Foundation:

• • "Universe as a Phase Boundary in a Four-Dimensional Euclidean Space", gr-qc/9805076.

and then expanded upon and given a more mathematical basis in 

• • "Quantum Mechanics, Quantum Gravity, and Approximate Lorentz Invariance from a Classical Phase-Boundary Universe", hep-th/0104237 (Ch. 3 in "Trends in Quantum Gravity Research," NOVA Science Publishers, 2006).

This proposal of a purely classical model has the potential to explain the origin of quantum mechanics, relativity, and even quantum gravity, but at this point is still more of a research proposal than a fully-fledged theory.   The expanding phase boundary means that our location in the fourth spatial dimension changes in lockstep, linearly, with the Newtonian time.  So we actually confuse this spatial dimension with time, resulting in a spatialization of time which births the Minkowski space of special relativity.  The randomness of the liquid we are moving into results in what we experience as quantum fluctuations. These are merely thermal fluctuations in the larger space (it is well known that quantum fluctuations can be modeled as thermal fluctuations in a classical model of one higher spatial dimension, for instance in lattice gauge theory).  The geometry of the surface itself can deviate from an exact sphere, which opens the possibility of explaining gravity through this geometry and its relationship to the growth rate.  If matter is viewed as dislocations in the crystal, then the fact that crystal growth is generally faster near dislocations allows one to possibly connect curvature to the presence of matter, but I have not succeeded in deriving general relativity from this.  Any theory of gravity that arose here would be a quantum theory because of the presence of the aforementioned thermal fluctuations.

Fermions could be something like screw dislocations and bosons like the photon would be phonons (sound waves).  However I am stuck on  the details of this because although screw dislocations in three dimensions look like particle world lines, in four dimensions they become sheets which aren't attractive candidates unless they are tightly wrapped like the strings of string theory, but I'm not convinced the crystal geometry allows this.   It is possible that the crystal/liquid interface is too simplistic, and other phases such as the complex phases of liquid He3 need to be considered (see book and papers by Volovnik). 

One aspect of this proposal that is very appealing to me is that it explains what the "present" is in physical terms.  Normal relativity theory denies the existence of the present as anything other than a human illusion, but our experience has a very difficult time reconciling this.  Another aspect of the proposal has the universe evolving classically, with the extra dimension presumably nullifying no-go theorems on hidden variable theories.  The past isn't totally frozen which allows quantum superpositions to exist as fluctuations in time that oscillate between possibilities.  If a symmetry is broken spontaneously, however then ergodicity is broken: the fluctuations are suppressed due to the very large numbers of degrees of freedom that are involved, and only one state is occupied.  This kind of time evolution allows one to model quantum measurements as spontaneous symmetry breaking events, and explains how superpositions are broken by a measurement.   The idea that spontaneous symmetry breaking is related to quantum measurement was developed in:

• • "Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement," hep-th/9409049 (1994).

These ideas were further developed in the context of the phase boundary universe proposal in:

• • "Two time solution to quantum measurement paradoxes," quant-ph/708.04275 (2017).

Many of the apparently paradoxical situations in entanglement and measurement theory become quite straightforward in this model, which is also a measurement theory compatible with special relativity.

I am currently working on simple models to better elucidate the generation of quantum theories from classical theories in one higher dimension.  Other loose ends involve identifying dislocations in four dimensional theories, and categorizing the phonon modes.  Finally, it would be satisfying to derive something like the Robertson-Walker-Friedmann universe from an underlying theory of crystal growth, as well as General Relativity from the surface geometry.

The big bang is just the nucleation event of the solid forming a crystal. Our notion of causality may require the crystal to grow at sonic or supersonic speed, to prevent signals sent into the crystal to ever come back to the surface, and prevent signals propagating forward into the liquid.  It is also possible to have several nucleation events near each other which would result in collisions of growing crystals.  The collisions would produce a lot of dislocations at the join boundary which is a 2d surface.  Matter in the present universe is mostly seen on a 2-d bubble network which could result from this.   A cosmic collision could also generate a lot of sound waves which after thermalization could explain the cosmic microwave background radiation.

It is almost impossible to come up with a full-fledged proposal that explains everything,  but personally I find these ideas quite satisfying, and happy to chip away at the problems one by one.

Latest Work:

Phase transitions in Gauge Higgs Models

I became interested in Gauge-Higgs models because some of the simpler ones allows one to further explore the presence of phase transitions in lattice gauge theories, even in the absence of obvious order parameters due to the local gauge symmetry.  My conclusion is that the local gauge symmetry hides the phase transitions but does not eliminate them.  Order parameters exist if the gauges are fixed.  The Higgs transitions are seen if one fixes to Landau gauge and the gauge (confinement) transition is seen if one fixes to Coulomb gauge.  Each of these gauge fixings leaves remnant global symmetries that can and do break spontaneously in phase transitions.  This topic was introduced in 

• • "Solution to the gauge-Higgs analyticity paradox," hep-lat/1502.04362 (2015).

and an extensive study of the 3D Z2 (Ising) gauge-Higgs theory is performed in:

• • "Exploring the 3D Ising gauge-Higgs theory in exact Coulomb gauge and with  a gauge-invariant substitute for Landau gauge," arXiv:2109.04560[hep-lat]

The 3D Ising-Gauge theory is particularly interesting for a couple of reasons. First it is self-dual, so that each phase transition has a dual reflection.  In particular the 3D Ising spin model at the Higgs-edge of the phase diagram is dual to the 3D Ising gauge theory on the gauge axis.  In Landau gauge, The Higgs Hamiltonian (phi)U(phi) where phi is the Higgs field and U is the gauge field is still mostly ferromagnetic at large gauge coupling beta, because Landau gauge seeks as many as possible of the U fields to be unity, and this is largely successful at high beta.  So the Higgs field sees only a scattering of antiferromagnetic links and its magnetic transition is largely unchanged as the phase diagram is entered.  The gauge transition can be monitored in Coulomb gauge.  Setting Coulomb gauge is usually quite difficult, involving simulated annealing or overrelaxation algorithms that often find a local rather than a global minumom.  This introduces systematic errors that can lead one to doubt any result.  However for this particular system, I found that the graph-theory Edmonds algorithm gives an exact solution in a reasonable computation time. This completely removes any objections to using Coulomb gauge to define an order parameter, which is simply the third component of the gauge field, treated as a spin. Coulomb gauge is similar to Landau but only the links in two of the three dimensions are optimized to unity. The Higgs and gauge transitions follow dual-related lines until the intersect.  At this point both transitions become first order and together run up the self-dual line a short ways, where the first order transition suddenly ends.   This much was known previously to my work (except for using the Coulomb gauge to follow the gauge transition).   Conventional wisdom had both phase transitions ending at this point, like a liquid-gas transition.  However, both the Higgs and gauge transitions are symmetry breaking, and symmetry breaking transitions of exact symmetries cannot ever end except at the edge of a phase diagram.  This is because the order parameter is exactly zero in the  random phase so in order to become non-zero it has to have a non-analytic point.  Setting Landau gauge is cumbersome and also subject to systematic errors, so I switched to an alternate procedure of using a two-real replica order parameter for the Higgs transition.  Here another "replica" Higgs field is introduced which is equilibrated to the gauge field background.  Then one looks at the overlap of the two Higgs fields, which will be non-zero in the frozen phase and zero in the random phase (if there were a spin-glass phase it would also be non-zero there but there is none for this system).  The replica procedure is fairly compute-intensive but more easily controlled than gauge fixing and I verified it gives the same results as Landau gauge fixing, but higher quality.   

If one looks beyond the end of the first order transition there is a surprise - the Higgs and gauge transitions split away from each other.  A further surprise is that they no longer follow dual-reflected paths.  This means there must be two more phase transition lines along the duals to these lines.  I questioned this result for a long time and took additional data, but concluded it simply had to be - a surprising degree of complexity for such a simple system to have six phases.  Later I discovered a possible reason for this (see next section on boundary percolation) .  I followed these transitions very far into the strong coupling region, to beta=0.05 and they could still be seen.   

It is quite disturbing that phase transitions seem to persist in this model because the Fradkin-Schenker  theorem based on work by Osterwalder and Seiler states that the Higgs phase and the confinement phase are analytically connected.  It is considered one of the few rigorously proven results in lattice theories.  Greensite has suggested that phase transitions seen with order parameters could become non-thermal, i.e. not be associated with singularities of the internal energy, entropy or other thermal quantities.  This would allow consistency with Fradkin-Shenkar. However I have shown this is only possible for certain values of critical exponents which can't happen here.  In fact I do see evidence of a thermal transition in third and higher moments of the internal energy.  Because the specific heat critical exponent is highly negative (~-2.5), these are not infinite singularities, but they can still be fit to.

So without really intending to, I seem to be challenging the Fradkin-Shenkar theorem.   Frankly it never made sense to me that the confinement and Higgs phases could be analytically connected because one is a random phase and the other is a frozen phase with a broken symmetry.  I studied the theorem for over a year. It uses a cluster expansion for which they proved convergence.  This proof of convergence seems good to me.  However I realized that the coefficients of the expansion themselves consisted of infinite-lattice expectation values similar to the average plaquette.  These are exactly the type of quantities that the theorem is trying to prove analytic.  Thus there appears to be a hidden assumption that the coefficients of the expansion are analytic functions of the couplings.  If they are not then the theorem breaks down even if the expansion converges.  Seiler claims that his Polymer Expansion does not have this flaw, but his paper seems to make a weaker claim than Fradkin-Shenkar, which would allow for a transition at an intermediate coupling.

Boundary Percolation and Phase transitions

I tried one more experiment which was to use the two-real replica order parameter in place of the Coulomb gauge fixing, in the same way as the same quantity for the Higgs field replaced Landau gauge fixing.  However, there was another surprise.  It sees a phase transition within the confining phase, where the Coulomb order parameter is zero.  This turns out to be a true spin-glass transition, which shows proper correlation-length scaling.  So this means there has to be a mirror transition in the dual theory, the venerable three dimensional Ising model, in its broken phase.  This would be  a dual-spin glass transition, whatever that entails. I searched for a long time for an order parameter for the Ising model itself, and finally hit upon "boundary percolation."  This is percolation of the plaquettes that make up the boundaries between domains of + and - spins.  I discovered that the boundary percolation transition occurs exactly on the dual-spin glass, and its shift-exponent agrees with the correlation length exponent of the spin-glass transition in the gauge theory.    This makes the existence of a new weak phase transition in the three-dimensional Ising model more believable, and gives a possible reason.   There is a formulation of the Ising model in terms of boundaries alone.  It seems reasonable that the entropy function could shift at the point of boundary percolation.   It was a surprise to me that the idea of boundary percolation had never been studied before, so I spent some time studying it in general, and am looking for other applications (I found one so far but not willing to talk about it yet). This work in the Ising model and its dual are given in

• • "Possible new phase transition in the 3D Ising model associated with boundary percolation," J. Phys. Condens. Matter 35 (2023) 285401 arXiv:2301.08424[cond-mat] (note: arXiv version slightly older).

The existence of these two new transitions on the axes means there are likely two more lines to draw on the phase diagram coming out of them.  These could join the others  at either end of the first order line (I I haven't studied this yet).  So now it is no longer such a surprise to have four transition lines beyond the first order line, since there are also now four lines in the portion of the diagram near the axes!  The extra phases are a Coulomb spin glass and the dual spin glass.