EFFECTIVE LAGRANGIAN OF PATH INTEGRAL QUANTIZATION FORMALISM IN CURVED SPACE

In this article the Weyl-McCoy correspondence of the classical Hamiltonian is extendedto curved space, and a general form of effective Lagrangian for path integral quantization incurved space is presented. To compare with the case in flat space, there need be in the Lee-Yang Lagrangian a metric correction term, which, being proportional to δ(0), is also a powerseries in δ(0). If a quantum mechanical Hamiltonian that is invariant under the point canonicaltransformation is demanded, a scalar curvature term will appear in the classical Lagrangianautomatically.