  We study a free particle system residing on a torus to investigate its
Becci-Rouet-Stora-Tyutin symmetries associated with its St\"uckelberg
coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric
geometry, we evaluate energy spectrum of the system to describe the particle
dynamics. We also investigate symplectic structures involved in the
second-class system on the torus.
