Particle production and complex path analysis
Abstract
This paper discusses particle production in Schwarzschildlike spacetimes and in a uniform electric field. Both problems are approached using the method of complex path analysis which is used to describe tunnelling processes in semiclassical quantum mechanics. Particle production in Schwarzschildlike spacetimes with a horizon is obtained here by a new and simple semiclassical method based on the method of complex paths. Hawking radiation is obtained in the (t,r) coordinate system of the standard Schwarzschild metric without requiring the Kruskal extension. The coordinate singularity present at the horizon manifests itself as a singularity in the expression for the semiclassical propagator for a scalar field. We give a prescription whereby this singularity is regularized with Hawking's result being recovered. The equation satisfied by a scalar field is also reduced to solving a onedimensional effective Schrödinger equation with a potential (1/x^{2}) near the horizon. Constructing the action for a fictitious nonrelativistic particle moving in this potential and applying the above mentioned prescription, one again recovers Hawking radiation. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely timedependent gauge. In a purely spacedependent gauge, however, the tunnelling interpretation has to be resorted to in order to recover the previous result. We attempt, in this paper, to provide a tunnelling description using the formal method of complex paths for both the time and space dependent gauges. The usefulness of such a common description becomes evident when ``mixed'' gauges, which are functions of both space and time variables, are analyzed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of elementary functions unlike the standard modes which are transcendental parabolic cylinder functions. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime.
 Publication:

Physical Review D
 Pub Date:
 July 1999
 DOI:
 10.1103/PhysRevD.60.024007
 arXiv:
 arXiv:grqc/9812028
 Bibcode:
 1999PhRvD..60b4007S
 Keywords:

 04.70.Dy;
 04.62.+v;
 12.20.m;
 Quantum aspects of black holes evaporation thermodynamics;
 Quantum field theory in curved spacetime;
 Quantum electrodynamics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 26 pages, Latex file, one eps figure