Quantum Mechanics on some Supermanifolds

L. MEZINCESCU

Valentin Lychagin

E. Gozzi

Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well‐known method of geometric quantization.

E. Gozzi, MAURO D.

Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. This form two grassmannian partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold, We prove that this procedure is equivalent to the well.known method of geometric quantization.

M. Kibler, Mohammed Daoud A

Maria Clara Nucci, P. G. L. Leach