Covariant phase space path integral

RAFAEL FERRARO; MAURICIO LESTON

Conferencia; Workshop; 7th International Conference Path Integrals: From Quarks to Galaxies; 2002

The quantum propagator K(q´,q) is a bidensity of weight 1/2 under general coordinate changes of its arguments. At the level of path integral this means that the measure should be a bidensity of weight 1/2 and the phase should be invariant. When path integration is performed in phase space, both requirements can be achieved by prescribing the skeletonization with the help of the Jacobi principal function (an invariant complete solution of the Hamilton-Jacobi equation that treats Riemann normal coordinates and momenta on an equal footing). The application of this prescription to a system defined on a riemannian geometry leads to the DeWitt curvature coupling in the Schrödinger equation.