Covariant and gauge-invariant calculation of higher-order corrections in WKB expansions on Riemannian manifolds
(1981) Physical Review D, Particles, Fields, Gravitation and Cosmology — Vol. 23, p. 1290 (1981)
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- (en) We show how to compute explicitly and in a covariant way the higher-order corrections to the WKB approximation for propagators in curved spaces. We treat the quantum propagator corresponding to the classical system with Lagrangian Lcl=(12)gμν˙qμ˙qν+˙qμAμ(q)−V(q). The method uses discrete techniques of phase-space functional integrals and involves normal coordinates around the classical path. The gauge invariance of the corrections is also explicitly exhibited.
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Langouche, F., Roekaerts, D., & Tirapegui, E. (1981). Covariant and gauge-invariant calculation of higher-order corrections in WKB expansions on Riemannian manifolds. Physical Review D, Particles, Fields, Gravitation and Cosmology, 23, 1290. https://doi.org/10.1103/PhysRevD.23.1290 (Original work published 1981)