Quantization in riemannian space

N.M. Chepilko, A.V. Romanenko

We use Nash embedding for Riemann smooth manifolds to propose a constrained phase space path integral for quantization of one particle motion in a Riemannian manifold.

H. Dekker

D. J. R. Lloyd-Evans

Эрнест Ахмеджанович Тагиров

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select a single rule of quantization is proposed by requirement of a consistency of the quantum mechanics' following from the canonical and quasiclassical approaches. This rule selects also a definition of the path integration. A geometric interpretation of the noncovariance of the canonical Hamilton operator of a particle with respect to the diffeomorphisms of the Riemannian configuration space is proposed.

Mircea Puta