dorsal/arxiv
View SchemaPerturbatively Defined Effective Classical Potential in Curved Space
| Authors | H. Kleinert, A. Chervyakov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301081 |
| URL | https://arxiv.org/abs/quant-ph/0301081 |
| DOI | 10.1142/S0217751X03016471 |
| Journal | Int.J.Mod.Phys. A18 (2003) 5521-5540 |
Abstract
The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average ${\bf x_0\equiv \beta ^{-1}\int_0^ \beta d\tau {\bf x}(\tau)$. We show how to generalize this concept to paths $q^\mu(\tau)$ in curved space with metric $g_{\mu \nu (q)$, and calculate perturbatively the high-temperature expansion of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate transformations $q^\mu(\tau)\to q'^\mu(\tau)$ introduces subtleties in the definition and treatment of the path average $q_0^\mu$, and covariance is achieved only with the help of a suitable Faddeev-Popov procedure.
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"abstract": "The partition function of a quantum statistical system in flat space can\nalways be written as an integral over a classical Boltzmann factor $\\exp[\n-\\beta V^{\\rm eff cl({\\bf x}_0)]$, where $V^{\\rm eff cl({\\bf x}_0)$ is the\nso-called effective classical potential containing the effects of all quantum\nfluctuations. The variable of integration is the temporal path average ${\\bf\nx_0\\equiv \\beta ^{-1}\\int_0^ \\beta d\\tau {\\bf x}(\\tau)$. We show how to\ngeneralize this concept to paths $q^\\mu(\\tau)$ in curved space with metric\n$g_{\\mu \\nu (q)$, and calculate perturbatively the high-temperature expansion\nof $V^{\\rm eff cl(q_0)$. The requirement of independence under coordinate\ntransformations $q^\\mu(\\tau)\\to q\u0027^\\mu(\\tau)$ introduces subtleties in the\ndefinition and treatment of the path average $q_0^\\mu$, and covariance is\nachieved only with the help of a suitable Faddeev-Popov procedure.",
"arxiv_id": "quant-ph/0301081",
"authors": [
"H. Kleinert",
"A. Chervyakov"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1142/S0217751X03016471",
"journal_ref": "Int.J.Mod.Phys. A18 (2003) 5521-5540",
"title": "Perturbatively Defined Effective Classical Potential in Curved Space",
"url": "https://arxiv.org/abs/quant-ph/0301081"
},
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