Production of Dirac particle in a deformed Minkowsky space-time

TL;DR

This paper investigates how a specific deformation of Minkowski space-time affects Dirac particles, analyzing vacuum pair creation probabilities and solving the modified Dirac equation in this context.

Contribution

It introduces a novel deformed Minkowski space-time model and explores its impact on Dirac field behavior and pair creation processes.

Findings

Deformation modifies the amplitude transition in vacuum pair creation.

The Dirac equation is explicitly solved in the deformed space-time.

Vacuum-vacuum pair creation probability density is derived.

Abstract

In this paper we study the Dirac field theory interacting with external gravitation field, described with tetrad of the form $e_b^\mu(x)=\varepsilon(\delta_b^\mu+\omega_{ba}^\mu x^a)$, where $\varepsilon=1$ for $\mu=0$ and $\varepsilon=i$ for $\mu=1,2,3.$ The probability density of the vacuum-vacuum pair creation is given. In particular case of vanishing electromagnetic fields, we point out how this deformation modify the amplitude transition. The corresponding Dirac equation is solved.