  We investigate all possible nilpotent symmetries for a particle on torus. We
explicitly construct four independent nilpotent BRST symmetries for such
systems and derive the algebra between the generators of such symmetries. We
show that such a system has rich mathematical properties and behaves as double
Hodge theory. We further construct the finite field dependent BRST
transformation for such systems by integrating the infinitesimal BRST
transformation systematically. Such a finite transformation is useful in
realizing the various theories with toric geometry.
