Journal ArticleDOI
On the stationary phase evaluation of path integrals in the coherent states representation
TLDR
In this paper, the authors derived a semiclassical formula for the coherent state propagator, which involves a path that is determined in exactly the same manner as the extremal paths of the conventional path integrals.Abstract:
The extremal paths that arise in the stationary phase evaluation of coherent state path integrals do not seem to have a simple physical interpretation, in contrast to the extremal paths that occur in the conventional path integrals. On the other hand, a recently derived semiclassical formula for the coherent state propagator involves a path that is determined in exactly the same manner as the extremal paths of the conventional path integrals. Since both the semiclassical and the stationary phase analyses yield asymptotic (h(cross) to 0) approximations, the stationary phase and the semiclassical expressions for the propagator should be identical. The author presents a simple and direct proof that, in spite of the apparent differences, this is indeed the case. The simplification in the semiclassical formula is due to the utilisation of an appropriate set of canonical variables to describe the classical dynamics. In order to illustrate the usefulness of the semiclassical formula they present an application to the problem of the degenerate parametric amplifier, which had been treated before by operator ordering and path integral methods. The semiclassical approach has a simple classical interpretation that is absent in the alternative treatments.read more
Citations
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Journal ArticleDOI
Coherent states: Theory and some Applications
TL;DR: In this article, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented, and the result is that the coherent states are isomorphic to a coset space of group geometrical space.
Journal ArticleDOI
Semiclassical approximations in phase space with coherent states
TL;DR: In this paper, a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space, is presented.
Journal ArticleDOI
Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves
Journal ArticleDOI
Semiclassical treatment of spin system by means of coherent states
TL;DR: In this article, a polygonal expansion of the discontinuous paths that enter the path integral is proposed to obtain the second-order coherent states for spin systems, and the results are in agreement with only one of the previous approaches, the one developed on Glauber's coherent states by means of a direct WKB approximation.
Journal ArticleDOI
Semiclassical theory of coherence and decoherence
TL;DR: In this article, a general semiclassical approach to quantum systems with system bath interactions is developed, and an effective system wavefunction emerges whose norm measures the decoherence and is equivalent to a density-matrix formulation.
References
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Coherent and incoherent states of the radiation field
TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
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Two-photon coherent states of the radiation field
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Large N limits as classical mechanics
TL;DR: In this article, a general method for finding classical limits in arbitrary quantum theories is developed, based on certain assumptions which isolate the minimal structure any quantum theory should possess if it is to have a classical limit.
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Path integrals and stationary-phase approximations
TL;DR: In this article, the general formalism for path integrals expressed in terms of an arbitrary continuous representation (generalized coherent states) is applied to give $c$-number formulations for the canonical algebra and for the spin algebra, and is used to derive meaningful stationary-phase approximations for these two cases.