Metaplectic operator approach to Gutzwiller's trace formula

Abstract

We derive the Gutzwiller's trace formula by considering the time-evolution operator of the Hamiltonian which describes an N-dimensional time-dependent generalized harmonic oscillator with general force terms, where the time-evolution operator is composed of metaplectic and Weyl-Heisenberg operators. The Hamiltonian is constructed by expanding a wave packet quadratically in position and momentum operators around a reference trajectory. Using the explicit form of the metaplectic operator recently obtained in (2022, J. Korean Phys. Soc. 80, 95), we give the proof of the well known properties of the metaplectic operator, and using those properties, we derive Gutzwiller's trace formula and investigate the Maslov index appearing in the formula.