Dunkl algebra and vacuum pair creation: Exact analytical results via Bogoliubov method

This paper examines the generation of scalar particle pairs resulting from the application of an external electric field's Coulomb potential in both three- and two-dimensional scenarios, employing Dunkl's formalism. In doing this, we present two distinct sets of exact solutions to the Dunkl-Klein-Gordon equation. Subsequently, we employ the canonical approach based on the Bogoliubov transformation to link the “in” and “out” states in order to compute both the probability of pair creation and the density of particle creation. It is shown that the conditions necessary for the creation of pairs of spinless particles depend on several factors: nucleus charge Z, quantum numbers, and Dunkl parameter. It is also shown that the Dunkl formalism enhances particle pair production.