dorsal/arxiv
View SchemaSemiclassical Series from Path Integrals
| Authors | C. A. A. de Carvalho, R. M. Cavalcanti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903028 |
| URL | https://arxiv.org/abs/quant-ph/9903028 |
| DOI | 10.1063/1.59667 |
| Journal | Trends in Theoretical Physics II (AIP Conference Proceedings 484), edited by H. Falomir, R. E. Gamboa Saravi, and F. A. Schaposnik (American Institute of Physics, Woodbury, 1999) pp 256-269 |
Abstract
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 Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ 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.
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"abstract": "We derive the semiclassical series for the partition function in Quantum\nStatistical Mechanics (QSM) from its path integral representation. Each term of\nthe series is obtained explicitly from the (real) minima of the classical\naction. The method yields a simple derivation of the exact result for the\nharmonic oscillator, and an accurate estimate of ground-state energy and\nspecific heat for a single-well quartic anharmonic oscillator. As QSM can be\nregarded as finite temperature field theory at a point, we make use of Feynman\ndiagrams to illustrate the non-perturbative character of the series: it\ncontains all powers of $\\hbar$ and graphs with any number of loops; the usual\nperturbative series corresponds to a subset of the diagrams of the\nsemiclassical series. We comment on the application of our results to other\npotentials, to correlation functions and to field theories in higher\ndimensions.",
"arxiv_id": "quant-ph/9903028",
"authors": [
"C. A. A. de Carvalho",
"R. M. Cavalcanti"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th"
],
"doi": "10.1063/1.59667",
"journal_ref": "Trends in Theoretical Physics II (AIP Conference Proceedings 484),\n edited by H. Falomir, R. E. Gamboa Saravi, and F. A. Schaposnik (American\n Institute of Physics, Woodbury, 1999) pp 256-269",
"title": "Semiclassical Series from Path Integrals",
"url": "https://arxiv.org/abs/quant-ph/9903028"
},
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