van Vleck determinants: Geodesic focusing in Lorentzian spacetimes

Matt Visser
Phys. Rev. D 47, 2395 – Published 15 March 1993
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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

Authors & Affiliations

Matt Visser*

  • Physics Department, Washington University, St. Louis, Missouri 63130-4899

  • *Electronic address: visser@kiwi.wustl.edu

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Vol. 47, Iss. 6 — 15 March 1993

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