Zeta-Functions and Star-Products
Frank Antonsen
Abstract
We use the definition of a star (or Moyal or twisted) product to give a phasespace definition of the ζ-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 αp2+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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