Quantum Mechanics on Simple Manifolds and Supermanifolds. Part I

Luca Mezincescu

Valentin Lychagin

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.

Philip Schuster, R. L. Jaffe

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.

Renzo Cirelli, Alessandro Manià, Livio Pizzocchero B

Making reference to the formalism developed in Part I to formulate Schrödinger quantum mechanics, the properties of Kählerian functions in general, almost Kählerian manifolds, are studied.