The Schwinger pair production method in the framework of non-commutative phase space coordinates and its applications

In noncommutative phase space (NCPS), we investigate the pair creation rate for the problem of scalar and spinorial particles emerging from a vacuum under the influence of uniform external electromagnetic fields using the Schwinger formal technique. It is demonstrated that under specific conditions, where the speed of light c approaches the Fermi velocity [Formula: see text] and [Formula: see text] (with [Formula: see text] representing the cyclotron frequency), the behavior of the Dirac oscillator problem in a uniform electromagnetic field within NCPS is akin to the monolayer graphene problem in NCPS. In addition, the production probability per unit volume per unit time is discussed, along with the limits of parameter deformations.