Coherent states expectation values as semiclassical trajectories

Journal Article · Tue Aug 15 04:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2227259· OSTI ID:20860753

Dias, N C; Mikovic, A; Prata, J N ^[1]

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1. Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. do Campo Grande, 376, 1749-024 Lisbon (Portugal)

We study the time evolution of the expectation value of the anharmonic oscillator coordinate in a coherent state as a toy model for understanding the semiclassical solutions in quantum field theory. By using the deformation quantization techniques, we show that the coherent state expectation value can be expanded in powers of ({Dirac_h}/2{pi}) such that the zeroth-order term is a classical solution while the first-order correction is given as a phase-space Laplacian acting on the classical solution. This is then compared to the effective action solution for the one-dimensional {phi}{sup 4} perturbative quantum field theory. We find an agreement up to the order {lambda}({Dirac_h}/2{pi}), where {lambda} is the coupling constant, while at the order {lambda}{sup 2}({Dirac_h}/2{pi}) there is a disagreement. Hence the coherent state expectation values define an alternative semiclassical dynamics to that of the effective action. The coherent state semiclassical trajectories are exactly computable and they can coincide with the effective action trajectories in the case of two-dimensional integrable field theories.

• OSTI ID: 20860753
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACTION INTEGRAL
ANHARMONIC OSCILLATORS
ANNIHILATION OPERATORS
COORDINATES
COUPLING CONSTANTS
DEFORMATION
EIGENSTATES
EXPECTATION VALUE
HARMONIC OSCILLATORS
INTEGRAL CALCULUS
LAPLACIAN
MATHEMATICAL EVOLUTION
MATHEMATICAL SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
PHASE SPACE
QUANTIZATION
QUANTUM FIELD THEORY
SEMICLASSICAL APPROXIMATION
TRAJECTORIES
TWO-DIMENSIONAL CALCULATIONS