Semiclassical Green functions in mixed spaces

Based on Maslov’s multidimensional semiclassical theory, a semiclassical Green function in a mixed position-momentum space is derived, which can be used to locally fix the semiclassical divergency in singular regions in configuration or momentum space. It is shown that when a semiclassical Green function is transformed from one representation to another, its form is invariant. The mixed representation includes both coordinate and momentum representations of semiclassical Green functions as two special cases.