A unique Fock quantization for fields in non-stationary spacetimes

In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics. Recently, however, some uniqueness results have been obtained for fields in non-stationary settings. In particular, for vacua that are invariant under the background symmetries, a unitary implementation of the classical evolution suffices to pick up a unique Fock quantization in the case of Klein-Gordon fields with time-dependent mass, propagating in a static spacetime whose spatial sections are three-spheres. In fact, the field equation can be reinterpreted as describing the propagation in a Friedmann-Robertson-Walker spacetime after a suitable scaling of the field by a function of time. For this class of fields, we prove here an even stronger result about the Fock quantization: the uniqueness persists when one allows for linear time-dependent transformations of the field in order to account for a scaling by background functions. In total, paying attention to the dynamics, there exists a preferred choice of quantum field, and only one $SO(4)$-invariant Fock representation for it that respects the standard probabilistic interpretation along the evolution. The result has relevant implications e.g. in cosmology.Comment: Typos correcte

Enhancing the movement of natural persons in the ASEAN region: Opportunities and constraints

The overall objective of the movement of natural persons (MNP) in the ASEAN region is to contribute to expanding trade in services and to deepening economic integration. However, the regional movement of human resources has proceeded beyond the expansion of trade and has persisted in response to labor market imbalances.Movement of Natural Persons (MNP),ASEAN Framework Agreements on Services (AFAS)

On effective loop quantum geometry of Schwarzschild interior

The success of loop quantum cosmology to resolve classical singularities of homogeneous models has led to its application to the classical Schwarszchild black hole interior, which takes the form of a homogeneous Kantowski-Sachs model. The first steps of this were done in pure quantum mechanical terms, hinting at the traversable character of the would-be classical singularity, and then others were performed using effective heuristic models capturing quantum effects that allowed a geometrical description closer to the classical one but avoided its singularity. However, the problem of establishing the link between the quantum and effective descriptions was left open. In this work, we propose to fill in this gap by considering the path-integral approach to the loop quantization of the Kantowski-Sachs model corresponding to the Schwarzschild black hole interior. We show that the transition amplitude can be expressed as a path integration over the imaginary exponential of an effective action which just coincides, under some simplifying assumptions, with the heuristic one. Additionally, we further explore the consequences of the effective dynamics. We prove first that such dynamics imply some rather simple bounds for phase-space variables, and in turn, remarkably, in an analytical way, they imply that various phase-space functions that were singular in the classical model are now well behaved. In particular, the expansion rate, its time derivative, and the shear become bounded, and hence the Raychaudhuri equation is finite term by term, thus resolving the singularities of classical geodesic congruences. Moreover, all effective scalar polynomial invariants turn out to be bounded.Comment: 26 pages, matches the PRD published versio

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.Comment: 11 pages, version accepted for publication in Classical and Quantum Gravit

Uniqueness of the Fock quantization of a free scalar field on S1S^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 $\ddot{\xi}-\xi"+f(t)\xi=0$. 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.Comment: 13 pages, typos corrected, version accepted for publication in Physical Review

Unitary evolution in Gowdy cosmology

Recent results on the non-unitary character of quantum time evolution in the family of Gowdy T**3 spacetimes bring the question of whether one should renounce in cosmology to the most sacred principle of unitary evolution. In this work we show that the answer is in the negative. We put forward a full nonperturbative canonical quantization of the polarized Gowdy T**3 model that implements the dynamics while preserving unitarity. We discuss possible implications of this result.Comment: 5 pages, no figures. V2 discussion expanded, references added. Final version to appear in PR