Fock quantization of a scalar field with time dependent mass on the three-sphere: Unitarity and uniqueness

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.044037· OSTI ID:21409323

Cortez, Jeronimo ^[1]; Mena Marugan, Guillermo A ^[2]; Velhinho, Jose M ^[3]

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1. Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Mexico D.F. 04510 (Mexico)
2. Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain)
3. Departamento de Fisica, Universidade da Beira Interior, R. Marques D'Avila e Bolama, 6201-001 Covilha (Portugal)

We study the Fock description of a quantum free field on the three-sphere with a mass that depends explicitly on time, also interpretable as an explicitly time dependent quadratic potential. We show that, under quite mild restrictions on the time dependence of the mass, the specific Fock representation of the canonical commutation relations which is naturally associated with a massless free field provides a unitary dynamics even when the time varying mass is present. Moreover, we demonstrate that this Fock representation is the only acceptable one, up to unitary equivalence, if the vacuum has to be SO(4)-invariant (i.e., invariant under the symmetries of the field equation) and the dynamics is required to be unitary. In particular, the analysis and uniqueness of the quantization can be applied to the treatment of cosmological perturbations around Friedmann-Robertson-Walker spacetimes with the spatial topology of the three-sphere, like e.g. for gravitational waves (tensor perturbations). In addition, we analyze the extension of our results to free fields with a time dependent mass defined on other compact spatial manifolds. We prove the uniqueness of the Fock representation in the case of a two-sphere as well, and discuss the case of a three-torus.

• OSTI ID: 21409323
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevD.81.044037; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CP INVARIANCE
DISTURBANCES
FIELD EQUATIONS
FOCK REPRESENTATION
GRAVITATIONAL WAVES
MASS
PERTURBATION THEORY
QUANTIZATION
QUANTUM FIELD THEORY
SCALAR FIELDS
SO-4 GROUPS
SPACE-TIME
SYMMETRY
TIME DEPENDENCE
TOPOLOGY
EQUATIONS
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICS
SO GROUPS
SYMMETRY GROUPS