Processus de creation de paires de particules et equations relativistes dependantes du temps.

Abstract

In this work, we are interested to the process of pair creation of spin 0 and 1/2 particle from the vacuum, by using the Schwinger technique based on the determination of the effective action and also on the obtaining of solution of Klein Gordon and Dirac equations when the potential has a dependency in vt, v being the velocity v (constant). In the process of pair creation, first a field of wave type Volkov and non-abelian with N generators (SU (N)) is considered in order to calculate analytically and algebraically the probability by using simple transformations. We have established for this form of interaction, that it is impossible to create particle pairs for the two cases of spin 0 and 1/2. In the framework of the geometry of the non-commutative spacetime, the same creation process is reconsidered with as interactions, the plane wave and the constant and uniform electromagnetic field. As a result, it was shown that the plane wave has no influence on the creative process and that the probability with a constant electric field is modified and that the magnetic field, only, can not create particle pairs. Finally, thanks to the invariance of Lorentz transformation the Klein Gordon and Dirac equations with a potential moving with a constant velocity v, it has been shown that solutions are obtained from these same equations with a static potential (not mobile) i.e. independent of time. As a special case, the form of potential "step" was considered mobile.