Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes

Journal Article · Sat Jan 15 00:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.025002· OSTI ID:21503976

Cortez, Jeronimo; Mena Marugan, Guillermo A; Olmedo, Javier; Velhinho, Jose M ^[1]

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1. Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Mexico D.F. 04510 (Mexico)

The Fock quantization of fields propagating in cosmological spacetimes is not uniquely determined because of several reasons. Apart from the ambiguity in the choice of the quantum representation of the canonical commutation relations, there also exists a certain freedom in the choice of field: one can scale it arbitrarily absorbing background functions, which are spatially homogeneous but depend on time. Each nontrivial scaling turns out into a different dynamics and, in general, into an inequivalent quantum field theory. In this work we analyze this freedom at the quantum level for a scalar field in a nonstationary, homogeneous spacetime whose spatial sections have S{sup 3} topology. A scaling of the configuration variable is introduced as part of a linear, time dependent canonical transformation in phase space. In this context, we prove in full detail a uniqueness result about the Fock quantization requiring that the dynamics be unitary and the spatial symmetries of the field equations have a natural unitary implementation. The main conclusion is that, with those requirements, only one particular canonical transformation is allowed, and thus only one choice of the field-momentum pair (up to irrelevant constant scalings). This complements another previous uniqueness result for scalar fields with a time varying mass on S{sup 3}, which selects a specific equivalence class of Fock representations of the canonical commutation relations under the conditions of a unitary evolution and the invariance of the vacuum under the background symmetries. In total, the combination of these two different statements of uniqueness picks up a unique Fock quantization for the system. We also extend our proof of uniqueness to other compact topologies and spacetime dimensions.

• OSTI ID: 21503976
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevD.83.025002; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CANONICAL TRANSFORMATIONS
COMMUTATION RELATIONS
COSMOLOGICAL MODELS
EVOLUTION
FIELD EQUATIONS
FOCK REPRESENTATION
MASS
PHASE SPACE
QUANTIZATION
QUANTUM FIELD THEORY
SCALAR FIELDS
SCALING
SPACE-TIME
SYMMETRY
TIME DEPENDENCE
TOPOLOGY
EQUATIONS
FIELD THEORIES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
SPACE
TRANSFORMATIONS