Super‐Selberg trace formula from the chaotic model

A nonrelativistic superparticle moving freely on the super‐Riemann surface of genus g≥2 is investigated. The classical motion is characterized by the super‐Fuchsian group. The periodic orbits are unstable and the system is classically chaotic. Quantization is performed in the path integral method. The kernel function is explicitly given in the semiclassical approximation. The quantized energy spectrum is related to the length spectrum of the classical periodic orbits, which is a superanalog of Selberg’s trace formula.