dorsal/arxiv
View SchemaZeta-Functions and Star-Products
| Authors | Frank Antonsen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9802031 |
| URL | https://arxiv.org/abs/quant-ph/9802031 |
Abstract
We use the definition of a star (or Moyal or twisted) product to give a phasespace definition of the $\zeta$-function. This allows us to derive new closed expressions for the coefficients of the heat kernel in an asymptotic expansion for operators of the form $\alpha p^2+v(q)$. For the particular case of the harmonic oscillator we furthermore find a closed form for the Green's function. We also find a relationship between star exponentials, path integrals and Wigner functions, which in a simple example gives a relation between the star exponential of the Chern-Simons action and knot invariants.
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"abstract": "We use the definition of a star (or Moyal or twisted) product to give a\nphasespace definition of the $\\zeta$-function. This allows us to derive new\nclosed expressions for the coefficients of the heat kernel in an asymptotic\nexpansion for operators of the form $\\alpha p^2+v(q)$. For the particular case\nof the harmonic oscillator we furthermore find a closed form for the Green\u0027s\nfunction. We also find a relationship between star exponentials, path integrals\nand Wigner functions, which in a simple example gives a relation between the\nstar exponential of the Chern-Simons action and knot invariants.",
"arxiv_id": "quant-ph/9802031",
"authors": [
"Frank Antonsen"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Zeta-Functions and Star-Products",
"url": "https://arxiv.org/abs/quant-ph/9802031"
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