Vincenzo Morinelli

Papers

Preprint

V. Morinelli, K.-H. Neeb, G. Ólafsson, Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality, arXiv:2508.10960 (2025)

The current article continues our project on representation theory, Euler elements, causal homogeneous spaces and Algebraic Quantum Field Theory (AQFT). We call a pair (h,k) of Euler elements orthogonal if $e^{\pi i \ad h} k = -k$. We show that, if (h,k) and (k,h) are orthogonal, then they generate a 3-dimensional simple subalgebra. We also classify orthogonal Euler pairs in simple Lie algebras and determine the fundamental groups of adjoint Euler elements in arbitrary finite-dimensional Lie algebras. Causal complements of wedge regions in spacetimes can be related to so-called twisted complements in the space of abstract Euler wedges, defined in purely group theoretic terms. We show that any pair of twisted complements can be connected by a chain of successive complements coming from 3-dimensional subalgebras.

Published in refereed journals

R. Longo, V. Morinelli, K.-H. Rehren, Where Infinite Spin Particles Are Localizable,
Commun. in Math. Phys., Volume 345, Issue 2, pp. 587-614 (2016). https://doi.org/10.1007/s00220-015-2475-9.

Infinite spin particle were in the 1939 Wigner classification of particle (unitary representation of the Poincaré group). Although they were never experimentally measured the problem of their localization property remained open. In this paper we solve this long-standing conjecture through operator algebraic methods: under natural assumptions there are no local observables and we discuss counterexamples.

V. Morinelli, Y. Tanimoto, M. Weiner, Conformal covariance and the split property,
Commun. Math. Phys. Volume 357, Issue 1, 379-406 (2018). https://doi.org/10.1007/s00220-017-2961-3.

Split property is the statistical independence for quantum systems. In this paper we prove that every chiral theory with diffeomorphism symmetry satisfy the Split property. We further discuss counterexamples.

V. Morinelli, The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions,
Ann. Henri Poincaré, Volume 19, Issue 3, 937-958 (2018). https://doi.org/10.1007/s00023-017-0636-4

The Bisognano-Wichmann property implies that the algebraic structure of the model contains all the information about the geometric symmetries of the theory. There is not a complete understanding, a general theorem, for this property. In this paper a new approach based on algebraic condition called "modularity condition" ensures it for second quantization models. Furthermore the "modularity condition" has very nice properties.

V. Morinelli, Y. Tanimoto, Scale and Möbius covariance in two-dimensional Haag-Kastler net,
Commun. in Math. Phys., Volume 371, Issue 2, 619–650 (2019), https://doi.org/10.1007/s00220-019-03410-x.

In Quantum field theory is a long-standing question whether scale invariance (dilation covariance) implies conformal covariance. This is expected, for instance after a massless scaling limit. Proofs on the physical side for chiral nets require strong assumptions or are incomplete. In this paper we prove the implication in the algebraic setting. Additional properties are either a certain condition on modular covariance, or a variant of strong additivity. The proof relies neither on the existence of stress-energy tensor nor any assumption on scaling dimensions. We further discuss counterexamples.

R. Longo, V. Morinelli, F. Preta, K.-H. Rehren, Split property for free finite helicity fields,
Ann. Henri Poincaré, Volume 20, Issue 8, 2555-2258 (2019). https://doi.org/10.1007/s00023-019-00820-4

Finite helicity representations extends to the conformal group. We decompose the restriction of any finite helicity representation to subgroup of conformal transformations fixing the time axis. This allows us to count the currents supported on the timeline of the associated free theory. We prove that higher helicity free theories satisfy the property of statistical independence, the Split property. The proof suggests new way to obtain higher helicity from lower helicity or scalar fields by a perturbation argument.

W. Dybalski, V. Morinelli, Bisognano-Wichmann property for asymptotically complete massless QFT
Commun. in Math. Phys. 380, 1267–1294 (2020). https://doi.org/10.1007/s00220-020-03755-8

We prove the Bisognano-Wichmann property for asymptotically complete Haag-Kastler theories of massless particles. These particles should either be scalar or appear as a direct sum of two opposite integer helicities, thus, e.g., photons are covered. The argument relies on a modularity condition formulated recently by me in "The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions," and on the Buchholz' scattering theory of massless particles.

V. Morinelli, K.-H. Rehren, Spacelike deformations: Higher-spin fields from scalar fields,
Letters in Mathematical Physics, 110, 2019–2038 (2020) https://doi.org/10.1007/s11005-020-01294-w

In contrast to Hamiltonian perturbation theory that changes the time evolution, "spacelike deformations" proceed by changing the translations (momentum operators). The free Maxwell theory is the first member of an infinite family of spacelike deformations of the complex massless Klein-Gordon quantum field into fields of higher spin.

V. Morinelli, and K.-H. Neeb, Covariant homogeneous nets of standard subspaces,
Commun. in Math. Phys., arXiv:2010.07128 (2021) https://doi.org/10.1007/s00220-021-04046-6

Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti-Guido-Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a Z2-graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag-Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries.

A. Stottmeister, V. Morinelli, G. Morsella, Y. Tanimoto, Scaling limits of lattice quantum fields by wavelets,
Commun. in Math. Phys. (2021), 387(1), pp. 299-360. https://doi.org/10.1007/s00220-021-04152-5

We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies' scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations.

A .Stottmeister, V. Morinelli, G. Morsella, Y. Tanimoto, Operator-algebraic renormalization and wavelets
Phys. Rev. Lett 127 (23), 230601, 6 pages, (2021). https://link.aps.org/doi/10.1103/PhysRevLett.127.230601

We report on a rigorous operator-algebraic renormalization group scheme and construct the free field with a continuous action of translations as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multi-scale entanglement renormalization ansatz and augments the semi-continuum limit of quantum systems.

V. Morinelli, Y. Tanimoto, B. Wegener, Modular operator for null plane algebras in free fields,
Commun. in Math. Phys. (2022). https://doi.org/10.1007/s00220-022-04432-8

We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of lightlike fibres and the modular operator decomposes accordingly. This implies that a certain form of QNEC is valid in free fields involving the causal completions of half-spaces on the null plane (null cuts). We also compute the relative entropy of null cut algebras with respect to the vacuum and some coherent states.

V. Morinelli, K.-H. Neeb, "A family of non-modular covariant AQFTs",
Analysis and Mathematical Physics 12, 124 (2022). https://doi.org/10.1007/s13324-022-00727-0

Based on the construction provided in our paper ``Covariant homogeneous nets of standard subspaces'', we construct {non-}modular covariant one-particle nets on the two-dimensional de Sitter spacetime and on the three-dimensional Minkowski space.

V. Morinelli, K.-H. Neeb, G. Olafsson, From Euler elements and 3-gradings to non-compactly causal symmetric spaces,
Journal of Lie theory, 33, No. 1, 377–432 (2023).
https://arxiv.org/abs/2207.14034

In this article we discuss the interplay between causal structures of symmetric spaces and geometric aspects of Algebraic Quantum Field Theory (AQFT). The central focus is the set of Euler elements in a Lie algebra, i.e., elements whose adjoint action defines a 3-grading. In the first half of this article we survey the classification of reductive causal symmetric spaces from the perspective of Euler elements. In the second half we obtain several results that prepare the exploration of the deeper connection between the structure of causal symmetric spaces and AQFT. Furthermore, we describe the group of connected components of the stabilizer group of Euler elements.

V. Morinelli, K.-H. Neeb, G. Olafsson, Modular geodesics and wedge domains in non-compactly causal symmetric spaces,
Annals of Global Analysis and Geometry, Volume 65, article number 9, (2024)
https://doi.org/10.1007/s10455-023-09937-6

Any Euler element of a semisimple Lie algebra specifies a canonical non-compactly causal symmetric space M = G/H, we turn in this paper to the geometry of this flow. Our main results concern the positivity region W of the flow (the corresponding wedge region): If G has trivial center, then W is connected, it coincides with the so-called observer domain, specified by a trajectory of the modular flow which at the same time is a causal geodesic, it can also be characterized in terms of a geometric KMS condition, and it has a natural structure of an equivariant fiber bundle over a Riemannian symmetric space that exhibits it as a real form of the crown domain of G/K. Among the tools that we need for these results are two observations of independent interest: a polar decomposition of the positivity domain and a convexity theorem for G-translates of open H-orbits in the minimal flag manifold specified by the 3-grading.

R. Longo, V. Morinelli, "An entropy bound due to symmetries",
Reviews in Mathematical Physics, (2024) Link arXiv:2401.02345

Let H be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime, covariant with respect to a positive energy, unitary representation U of the Poincaré group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy S of a vector in a region that depends only on U and the PCT anti-unitary canonically associated with H. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the U(1)-current derivatives.

V. Morinelli, K.-H. Neeb, "From local nets to Euler elements",
Advances in Mathematics, Volume 458, Part A, (2024) https://doi.org/10.1016/j.aim.2024.109960

Various aspects of the geometric setting of Algebraic Quantum Field Theory (AQFT) models related to representations of the Poincaré group can be studied for general Lie groups, whose Lie algebra contains an Euler element, i.e., ad h is diagonalizable with eigenvalues in {-1,0,1}. This has been explored by the authors and their collaborators during recent years. A key property in this construction is the Bisognano-Wichmann property (thermal property for wedge region algebras) concerning the geometric implementation of modular groups of local algebras.In the present paper we prove that under a natural regularity condition, geometrically implemented modular groups arising from the Bisognano-Wichmann property, are always generated by Euler elements. We also show the converse, namely that in presence of Euler elements and the Bisognano-Wichmann property, regularity and localizability hold in a quite general setting. Lastly we show that, in this generalized AQFT, in the vacuum representation, under analogous assumptions (regularity and Bisognano-Wichmann), the von Neumann algebras associated to wedge regions are type III_1 factors, a property that is well-known in the AQFT context.
17. V. Morinelli, A geometric perspective on Algebraic Quantum Field Theory, arXiv:2412.20410, To appear in Journal of Lie Theory

In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. Ólafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental concepts and some of the relevant results about the abstract structure of these models are here presented.

18. C. Dappiaggi, V. Morinelli, G. Morsella, A. Ranallo, The modular Hamiltonian in asymptotically flat spacetime conformal to Minkowski, To appear in Communications in Mathematical Physics arXiv:2505.20191

We consider a four-dimensional globally hyperbolic spacetime (M,g) conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of an injective *-homomorphism between , the Weyl algebra of observables on and a counterpart which is defined intrinsically on future null infinity, a component of the conformal boundary of M. We can individuate thereon a distinguished two-point correlation function whose pull-back on M to identifies a quasi-free Hadamard state for the bulk algebra of observables. In this setting, if we consider V, a future light cone, its counterpart at the boundary is the Weyl subalgebra generated by suitable functions localized in a positive half strip on the boundary. To each such cone, we associate a standard subspace of the boundary one-particle Hilbert space. We extend such correspondence by considering deformed cones. This result allows us to study the relative entropy between coherent states of the algebras associated to the deformed cones establishing the quantum null energy condition.

Contribute in Conference Proceedings

V. Morinelli, An algebraic condition for the Bisognano-Wichmann Property,
Proceedings of the 14th Marcel Grossmann Meeting - MG14, Rome pp. 3849-3854 (2017) https://doi.org/10.1142/9789813226609_0509.

I anticipated some of the results that are described in "The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions"

V. Morinelli, "Standard subspaces in Representation Theory",
Mini-Workshop: Standard Subspaces in Quantum Field, Report No. 50/2023, DOI: 10.4171/OWR/2023/50
report on the joint works with K.-H. Neeb (FAU Erlangen-Nürnberg) and G. Ólafsson (Louisiana State University)

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