A unique Fock quantization for fields in non-stationary spacetimes

Journal Article · Fri Oct 01 04:00:00 EDT 2010 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2010/10/030· OSTI ID:22275360

Cortez, Jerónimo ^[1]; Marugán, Guillermo A. Mena; Olmedo, Javier ^[2]

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1. Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico)
2. Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain)

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.

• OSTI ID: 22275360
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 10 Vol. 2010; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COSMOLOGICAL MODELS
COSMOLOGY
DIAGRAMS
FOCK REPRESENTATION
KLEIN-GORDON EQUATION
MASS
PROBABILISTIC ESTIMATION
QUANTIZATION
QUANTUM FIELD THEORY
SPACE-TIME
SYMMETRY
TIME DEPENDENCE
TRANSFORMATIONS