Semiclassical Expansions on Riemannian Manifolds

Abstract

Given the differential equation $(Q = ({Q^{1}},{Q^{2}},...,{Q^{M}}),{\kern 1pt} \partial ) \equiv \partial /\partial Q)$

$$\frac{\partial }{{\partial t}}p\left( {Q,t} \right) = \mathfrak{L}\left( {Q,\partial ,n} \right)p\left( {Q,t} \right)$$

(1)

where L(Q, ∂, η) contains at most second derivatives and η is a small parameter, one is interested in the propagator of (1), i.e. the solution I(Q,t;Q₀,t₀) such that I(Q, t;Q₀,t) = δ(Q-Q₀).