Abstract
The van Vleck determinant is a ubiquitous object, arising in many physically interesting situations such as (1) WKB approximations to quantum time evolution operators and Green functions, (2) adiabatic approximations to heat kernels, (3) one-loop approximations to functional integrals, (4) the theory of caustics in geometrical optics and ultrasonics, and (5) the focusing and defocusing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. A fortiori these developments have important implications for the entire array of topics indicated.
- Received 13 November 1992
DOI:https://doi.org/10.1103/PhysRevD.47.2395
©1993 American Physical Society