arXiv subjects

Guillermo A. Mena Marugán

Publications and source records attributed to Guillermo A. Mena Marugán.

78 records · Page 5Linked to original sources

arXiv2011

A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that, when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time dependent mass.

gr-qc↗

arXiv2010

Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model

We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy $T^3$ model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of matter content, the application of loop techniques leads to a quantum resolution of the classical cosmological singularity. Most importantly, thanks to the inclusion of matter, the homogeneous sector of the model contains flat Friedmann-Robertson-Walker (FRW) solutions, which are not allowed in vacuo. Therefore, this model provides a simple setting to study at the quantum level interesting physical phenomena such as the effect of the anisotropies and inhomogeneities on flat FRW cosmologies.

gr-qc↗

arXiv2010

Hybrid Quantization: From Bianchi I to the Gowdy Model

The Gowdy cosmologies are vacuum solutions to the Einstein equations which possess two space-like Killing vectors and whose spatial sections are compact. We consider the simplest of these cosmological models: the case where the spatial topology is that of a three-torus and the gravitational waves are linearly polarized. The subset of homogeneous solutions to this Gowdy model are vacuum Bianchi I spacetimes with a three-torus topology. We deepen the analysis of the loop quantization of these Bianchi I universes adopting the improved dynamics scheme put forward recently by Ashtekar and Wilson-Ewing. Then, we revisit the hybrid quantization of the Gowdy $T^3$ cosmologies by combining this loop quantum cosmology description with a Fock quantization of the inhomogeneities over the homogeneous Bianchi I background. We show that, in vacuo, the Hamiltonian constraint of both the Bianchi I and the Gowdy models can be regarded as an evolution equation with respect to the volume of the Bianchi I universe. This evolution variable turns out to be discrete, with a strictly positive minimum. Furthermore, we argue that this evolution is well-defined inasmuch as the associated initial value problem is well posed: physical solutions are completely determined by the data on an initial section of constant Bianchi I volume. This fact allows us to carry out to completion the quantization of these two cosmological models.

gr-qc↗

arXiv2009

Uniqueness of the Fock quantization of a free scalar field on $S^1$ with time dependent mass

We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the form $\ddotξ-ξ"+f(t)ξ=0$. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field ($f=0$) provides a unitary implementation of the dynamics for sufficiently general mass terms, $f(t)$. Furthermore, this representation is uniquely specified, among the class of representations determined by $S^1$-invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections.

gr-qc↗

arXiv2004

Asymptotics of Regulated Field Commutators for Einstein-Rosen Waves

We discuss the asymptotic behavior of regulated field commutators for linearly polarized, cylindrically symmetric gravitational waves and the mathematical techniques needed for this analysis. We concentrate our attention on the effects brought about by the introduction of a physical cut-off in the study of the microcausality of the model and describe how the different physically relevant regimes are affected by its presence. Specifically we discuss how genuine quantum gravity effects can be disentangled from those originating in the introduction of a regulator.

gr-qc↗

arXiv2004

Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves

We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry out our analysis. Field commutators are used here to analyze microcausality, in particular the smearing of light cones owing to quantum effects. We discuss in detail several issues related to the semiclassical limit of quantum gravity, in the simplified setting of the cylindrical symmetry reduction considered here. We show, for example, that the small G behavior is not uniform in the sense that its functional form depends on the causal relationship between spacetime points. We consider several physical issues relevant for this type of models such as the emergence of large gravitational effects.

gr-qc↗