Production of Dirac particle in a deformed Minkowsky space-time

In this paper we study the Dirac field theory interacting with external gravitation field, described with tetrad of the form $e_b^μ(x)=\varepsilon(δ_b^μ+ω_{ba}^μx^a)$, where $\varepsilon=1$ for $μ=0$ and $\varepsilon=i$ for $μ=1,2,3.$ 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.

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