Uniqueness of the Fock quantization of a free scalar field on S{sup 1} with time dependent mass

Journal Article · Wed Apr 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.084040· OSTI ID:21308334

Cortez, Jeronimo; Marugan, Guillermo A. Mena; Serodio, Rogerio; Velhinho, Jose M ^[1]

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1. Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, A. Postal 50-542, Mexico D.F. 04510 (Mexico)

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 {xi}-dot-dot-{xi}{sup ''}+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{sup 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.

• OSTI ID: 21308334
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 79; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AXIAL SYMMETRY
COMMUTATION RELATIONS
COSMOLOGY
MASS
POLARIZATION
POTENTIALS
QUANTIZATION
SCALAR FIELDS
TIME DEPENDENCE
WAVE EQUATIONS