Semiclassical series from path integrals

Journal Article · Tue Jul 13 04:00:00 EDT 1999 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.59667· OSTI ID:21210420

Cavalcanti, R M ^[1]

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1. Instituto de Fisica, Universidade Federal do Rio de Janeiro, Cx. Postal 68528, CEP 21945-970, Rio de Janeiro, RJ (Brazil)

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of the field-theoretic language of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of ({Dirac_h}/2{pi}) and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.

• OSTI ID: 21210420
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 484; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANHARMONIC OSCILLATORS
CORRELATION FUNCTIONS
FEYNMAN DIAGRAM
GROUND STATES
HARMONIC OSCILLATORS
PARTITION FUNCTIONS
PATH INTEGRALS
PERTURBATION THEORY
POTENTIALS
QUANTUM FIELD THEORY
SEMICLASSICAL APPROXIMATION
SPECIFIC HEAT
STATISTICAL MECHANICS