1998/02/12 by Frank Antonsen, Antonsen, Frank
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9802031
LaTeX2e with 2 Postscript figures
arxiv created 1998/02/12 · arxiv updated 2009/11/30
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.