The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory

Journal Article · Mon Jun 15 00:00:00 EDT 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.03.003· OSTI ID:21308060

Villasenor, Eduardo J.S. ^[1]

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1. Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain)

In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schroedinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models.

• OSTI ID: 21308060
• Journal Information: Annals of Physics (New York), Vol. 324, Issue 6; Other Information: DOI: 10.1016/j.aop.2009.03.003; PII: S0003-4916(09)00058-X; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COSMOLOGICAL MODELS
EIGENSTATES
EVOLUTION
HARMONIC OSCILLATORS
ONE-DIMENSIONAL CALCULATIONS
OSCILLATORS
PROBABILITY
PROPAGATOR
QUANTUM FIELD THEORY
SCALAR FIELDS
SCHROEDINGER PICTURE
SEMICLASSICAL APPROXIMATION
TIME DEPENDENCE
TRANSITION AMPLITUDES
UNITARITY