Abstract
This work addresses the computation of the probability of fermionic particle pair production in \((d+1)\)-dimensional noncommutative Moyal space. Using Seiberg–Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter \(\theta \), we derive the probability density of vacuum–vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed.
Highlights
Noncommutative field theory (NCFT), arising from noncommutative (NC) geometry, has been the subject of intense studies, owing to its importance in the description of quantum gravity phenomena
The concepts of the noncommutativity in fundamental physics have deep motivations which originated from the fundamental properties of the Snyder space–time [1]
The results by Connes et al [2–4] provided a clear definition of NC geometry, bringing about a new stimulus in this area
Summary
Noncommutative field theory (NCFT), arising from noncommutative (NC) geometry, has been the subject of intense studies, owing to its importance in the description of quantum gravity phenomena. Apart from the overall results as regards QED and YM theory in NC space–time, it turns out to be important to understand how noncommutativity modifies the probability of pair production of fermionic particles. This is the task we shall deal with in this work. We derive the exact expression for the probability density of particle production by an external field This establishes a relation with important analytical results which were previously obtained in ordinary space– time, spread in the literature [22,23,25–27,31]. Appendices A and B are for proofs of the key theorems in the main part of this paper
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