Particle creation in the presence of minimal length: The time dependent gauge

Abstract

In this paper we have studied the problem of scalar particles pair creation by a constant electric field in the presence of a minimal length. A closed expression for the corresponding Green's function is obtained via path integral approach. Then by projecting this function on the outgoing particle and antiparticle states we have calculated the probability to create a pair of particles and the number density of created particles. From this, we have deduced the modifications brought by the minimal length to Hawking temperature and black hole entropy. It is shown that the first correction is a logarithmic term with a negative numerical factor. We have also examined the semiclassical WKB approximation in the calculation of the pair production rate. The result is that, unlike the ordinary case, the WKB approximation in the presence of a minimal length does not give the exact rate even for the constant electric field.