Talks

Mini course:

Mariano Celada: "BF gravity"

This talk is devoted to a classical description of the BF formulations of general relativity and their relation to other formulations thereof.

Plenary talks:

• Suzanne Lanery: "The DIY Quantum Field Theory"

I will describe how to build a Quantum Field Theory from scratch using easy-to-source parts (aka. finite dimensional quantum theories). The tools of choice are Jerzy Kijowski's projective construction for QFT and Robert Oeckl's General Boundary Formulation. Special options, such as a curved background spacetime or explicit access to the semi-classical sector, can be accommodated. However, be warned that to assemble a non-linear QFT, some extra tools will in general be needed (aka. renormalization).

• Diego González: "Reformulation of the symmetries of first-order general relativity"

In this talk, we will use the converse of Noether's second theorem to uncover a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term that can be regarded as the natural extension of the three-dimensional local translations. The new symmetry can be taken as a fundamental gauge symmetry of general relativity instead of diffeomorphisms, which can be expressed as linear combinations of the new symmetry and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. Also, we will present the analog of the new gauge symmetry for the Holst action, showing that it explicitly depends on the Immirzi parameter. Finally, we will consider the non-minimal coupling of a scalar field to gravity and show that the new gauge symmetry is affected by this matter field.

• Yuri Bonder: "Quantum Gravity Phenomenology: From a systematic approach to LQG applications"

Quantum Gravity Phenomenology (QGP) is a program in which the main goal is to find empirical clues of quantum gravity. I will present a systematic "algorithm" for QGP where the key step is to use a general parametrization describing all the possible effects associated with violating a principle of conventional physics. This step allows one to perform self-consistency tests and to compare bounds obtained with different experiments. As an example, I will discuss the phenomenological program to test local Lorentz invariance. On the other hand, when there are concrete quantum gravity predictions, one can try to look for them directly. In this context I will describe an analysis where the electromagnetic field is "polymerically" quantized and the model predictions are compared with GRB observations.

Contributed talks:

• Alejandro Corichi: "Bounce times in black hole bounce"
• Saeed Rastgoo: "The continuum limit of metric spaces: a renormalization framework for the emergence of space(time)"

I present a novel method to obtain the continuum limit of graphs and metric spaces. It is based on the process of renormalization and employs several concepts such as Gromov-Hausdorff distance and ideas from geometric group theory. I discuss the framework and its current results, its implications about the structure of space(time), its emergence and its dimension, and other concepts such as nonlicality and entanglement. Finally, I will talk about the challenges and plans ahead.

• Homero G. Díaz-Marín: "Campos de Yang-Mills en variedades riemannianas, caso abeliano"
• Robert Oeckl: "Predictions in quantum gravity"

Unlike in classical physics, measurement is a primitive notion in quantum theory. Explaining how measurement outcomes can be predicted is thus a fundamental task of any quantum theory, including any quantum theory of gravity. Existing approaches have struggled with this basic requirement. However, recent progress on the foundations of quantum theory has led to a much better understanding of how predictions in quantum gravity can be made in principle. Rather than discussing the underlying framework, as I have done in many previous talks, in this talk I want to focus on a concrete example: A black hole bounce. This also illustrates where certain traditional approaches fail.

• José A. Zapata: "Loop quantum gravity and topological charges in discretized gauge theories"

Loop quantization is a framework under construction designed to quantize gauge theories applicable in particular general relativity seen as a theory of gauge fields. The starting point of this quantization framework is a description of gauge fields over discretizations of space and/or spacetime; they constitute truncations of the space of gauge fields in the continuum in the sense of real space renormalization.

Recently we proposed a refinement of this truncation in which by adding a discrete set of variables to the usual parallel transport variables the gauge field at each scale becomes a certain homotopy class of gauge fields in the continuum.

The work presented today shows how to extract the topological invariants usually called ``topological charges’’ from an (extended) loop quantized field. These results show the power of our refinement of the truncation at a given scale. At a more concrete level, they provide exact regularizations of: (i) two dimensional quantum gravity, and also of (ii) ``partial boundary terms'’ for quantum gravity in four dimensions needed in the presence of certain types of horizons.

In collaboration with Claudio Meneses.

• Jasel Berra-Montiel: "Polymer quantum mechanics as a deformation quantization"

The polymer representation of quantum mechanics is obtained by quantizing a mechanical system adapting the techniques used in Loop Quantum Gravity. In this talk, we analyze the polymer representation within the framework of deformation quantization. The idea behind deformation quantization relies on a deformation of geometrical structures of the classical phase space, such as the Poisson bracket and the algebra of observables, resulting that the states are no longer elements in a Hilbert space, but they behave as pseudo-probability distributions defined on phase space. We discuss some properties of these deformed structures and the possible relations between loop quantization and non-commutativity.

• Alberto Molgado: "MacDowell-Mansouri gravity model from a covariant polysymplectic perspective"

Traditionally, classical field theories have been successfully analyzed either at a Lagrangian or at a Hamiltonian level. However, the introduction of a canonical formulation that includes a covariant Poisson bracket has not been satisfactorily presented so far within these perpspectives. In this sense, based on the foundations of the variational calculus and the multisymplectic geometry, in this talk we will consider the polysymplectic formalism which allows us to incorporate a classical Poisson structure adapted to the covariant De Donder-Weyl equations associated to a given field theory. In particular, we will emphasize the application of the polysymplectic formalis for the description of the MacDowell-Mansouri model for gravity which consists on a Yang-Mills-type gauge theory with gauge group SO(4,1) that after symmetry breaking turns out to be classically equivalent to the standard Palatini action for General Relativity. For this model we will describe the way in which the polysymplectic formalism adapts to the emerging constraints and also how the symmetry breaking process is implemented.

• Elías Castellanos Alcántara: "Polymer Bose-Einstein condensates; a phenomenological approach"
• Juan Daniel Reyes: "Canonical formulation from the Holst action for Weakly Isolated Horizons"

As a prerequisite for quantization, state counting calculations for the entropy of black holes in LQG require a well defined Hamiltonian formulation in connection variables, compatible with horizon boundary conditions. The celebrated results of black hole entropy in LQG start from the self-dual action and restrict to the special spherically symmetric Type I isolated horizon. No complete or clean derivation of the canonical Hamiltonian framework in real (or complex) variables exists for more general o realistic isolated horizons.

In this talk we argue about the necessity of such classical canonical formulation. We discuss the technical complications involved in its construction and state some preliminary results on the internal gauge freedom.

• Ricardo Rosas Rodríguez: "El Bracket de Kauffman como una Solución de las Constricciones de la Relatividad General con Constante Cosmológica"
• Víctor Hugo Flores Soto: "Haciendo gravedad cuantica 3-d en la formulación de fronteras generales"