Schwinger's Result On Particle Production From Complex Paths WKB Approximation

Details Schwinger's Result On Particle Production From Complex Paths WKB Approximation Schwinger's Result On Particle Production From Complex Paths WKB Approximation

1999-06-18

arxiv.org/abs/gr-qc/9906081v1

Int.J.Mod.Phys. A15 (2000) 3717-3732

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 Pages, LaTeX, no figure

Scientific paper

10.1142/S0217751X0000122X

This paper presents the derivation of Schwinger's gauge invariant result of $Im \cal{L}_{eff}$ upto one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation (CWKB). The CWKB proposed by one of the author's \cite{bis:ijtp} looks upon particle production as due to the motion of a particle in complex space-time plane, thereby requiring tunneling paths both in space and time. Recently \cite{srini:iucaa,srini1:iucaa} there have been some efforts to calculate the reflection and transmission co-efficients for particle production in uniform electric field that differ from our expressions for the same. In this paper we clarify the confusion in this regard and establish the correctness of CWKB.

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