The seminar is organized by Robert Oeckl and held at the CCMUNAM in Morelia.
date  time  place  speaker  title (click for abstract) 

0802  17:00  Salón 4  Suzanne Lanéry (CCMUNAM)  X
In the previous two talks of this series (on May 24 and June 28), it was discussed how quantum transition amplitudes can be obtained through the imposition of suitable first class constraints. In the case of a finitedimensional linear system, this perspective provides an unambiguous prescription to derive the correct amplitude. The key to lift these results to the infinitedimensional case is to understand an infinitedimensional linear theory (aka. free field theory) as a consistent collection of finitedimensional ones:

0823  17:00  Salón 4  Benito Alberto Juárez Aubry (ICNUNAM)  X
We show how to associate natural boundary Hilbert spaces to the quantisation of classical systems in bounded regions that can be understood as composite boundarybulk systems. As an example, we will show in detail how one can Fock quantise a linear fieldparticle interacting system consisting of a string with two point masses attached at the ends. We shall see that, although the quantised system cannot be immediately decomposed as a tensor product of 'masses' and 'string' Hilbert spaces, there is a natural Hilbert space that can be associated to the boundary with the aid of socalled trace operators from PDE theory. 
0922  11:00  Salón 6  Claudio Meneses Torres (CIMAT)  X
Let G be a simplyconnected, compact, simple Lie group (such as the special unitary groups SU(n)), and let M be a 4dimensional, compact and oriented smooth manifold. It is a standard fact that the space of equivalence classes of principal Gbundles P > M is parametrized by a single topological invariant, the socalled "topological charge" in the physics jargon, which corresponds to an integer. This talk will begin with a brief introduction to the previously mentioned notions, and then I will describe work in progress with José A. Zapata, on the reconstruction of such topological invariants in the context of extended lattice gauge fields, a formalism that we have introduced to enhance the discretization mechanism of gauge theories, in such a way that each ELG field corresponds to a certain homotopy class of gauge fields in the continuum. The reconstruction is motivated by analogous ideas in 2dimensional abelian topological gauge theory. 
1004  17:00  Salón 4  Robert Oeckl (CCMUNAM)  X
At the end of the 1980s the concept of topological quantum field theory (TQFT), motivated originally from physics and due to Witten, Atiyah, Segal and others, originated a revolution in algebraic topology, knot theory and other areas. In particular, TQFTs serve in the construction of invariants of manifolds and of knots. I discuss a new class of topological quantum field theories that I call "positive TQFTs". In these the objects associated to hypersurfaces are ordered vector spaces and the morphisms associated to cobordisms are completely positive linear maps. I describe a functorial construction that converts "ordinary" TQFTs into positive TQFTs by "taking the modulus square". An attractive feature of positive TQFTs is that they provide an inherent means of dealing with infinities. This means in particular that one can work with infinite dimensional vector spaces in a well defined way, rather than only with finite dimensional ones as is customary. One could hope that this may lead to new invariants of manifolds for example. 
1018  12:30  Salón 8  Suzanne Lanéry (CCMUNAM)  X
Instead of formulating the states of a Quantum Field Theory (QFT) as vectors in a single large Hilbert space (or, more generally, density matrices thereon), it has been proposed by Kijowski to construct them as *consistent* families of *partial* density matrices, the latter being defined over *small* 'building block' Hilbert spaces. In this picture, each small Hilbert space can be physically interpreted as extracting from the full theory specific degrees of freedom (aka. 'coarsegraining' the continuous theory). The resulting quantum state spaces tend to be more robust than those obtained via ordinary Focklike constructions: they allow to bypass vacuum ambiguities, facilitate the systematic construction of semiclassical states and support a wide range of dynamics. I will give an introduction to this framework, illustrating it on the example of polymer quantization (as used in isotropic LQC). In particular, I will discuss how the thus obtained quantum state space relates to the Schrödinger representation and the Bohr compactification one respectively, and I will comment on how these techniques could help deepen the LQC/LQG connection (in particular at the dynamical level). 
1121  17:00  Salón 8  Hugo Ferreira (INFN Pavia, Italy)  X
Antide Sitter is not a globally hyperbolic spacetime. When studying a field theory in antide Sitter, one needs an appropriate choice of boundary conditions at the conformal boundary such that the classical field equation is wellposed. Moreover, at the level of the standard formulation of quantum field theory, the existence of physical quantum states, the socalled Hadamard states, is only guaranteed (and defined) on globally hyperbolic spacetimes. In this talk, I discuss the classical and quantum theory of a real, massive scalar ﬁeld in the Poincaré patch of the (d+1)dimensional antide Sitter spacetime, with arbitrary, Robin boundary conditions (including the commonly used Dirichlet boundary conditions). We show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, timeslice axiom and Flocality. In addition, we characterize the wavefront set of the ground state associated to this system. As a consequence, we are able to generalize the deﬁnition of Hadamard states and construct a global algebra of Wick polynomials. 
1122  17:00  Salón 4  Benito Alberto Juárez Aubry (ICNUNAM)  X
Dynamical reduction models have been proposed in (nonrelativistic) quantum mechanics to deal with the socalled measurement problem by modifying the Schrödinger evolution equation and including nonunitary terms, which induce the 'spontaneous collapse' of the wavefunction of a system. In this talk, we shall show some recent developments in generalising these models to quantum field theory in curved spacetimes. An important obstruction in this generalisation is the possibility that an initial Hadamard state of a free theory could evolve into a nonHadamard one, rendering the model unacceptable. We show that, for a large class of models, this problem does not arise and the Hadamard property is preserved. Based on: [arXiv:1708.09371 [grqc]]. 
1213  12:00  Salón 3  Ángel Alejandro García Chung (UAM)  X
The polymer harmonic oscillator is a toy model mimicking some of the techniques used in LQG. Among other features, it is a nonregular representation of the Weyl algebra. This makes unclear what the symmetry group of this model is. In this talk, we will show the first steps to answer this question. 
Last updated 13 December 2017.