Feynman path integrals on phase space and the metaplectic representation
The authors create some analogue of Feynman's path integral approach to quantum mechanics but they use paths in phase space rather than in configuration space and use the symplectic action integral rather than the classic Lagrangian integral. The main difference with respect to other investigations in this direction is that the authors consider (inhomogeneous) quadratic Hamiltonians which allows them to obtain some new results. In particular they obtain Leray's formula for the metaplectic representation.
scientific article; zbMATH DE number 861953
scientific article