Résumé:
In our thesis, we have presented an exact analytical solution of the massless Dirac-Graphene equation in the presence of two plane wave fields using Volkov's ansatz. We have adapted also the supersymmetric path integral formalism for constract the corrsponding Dirac-Graphene propagator. Finally, the wave functions are deduced. On the other hand, we have studied the problem of Graphene's quasiparticle-hole pair creation from the vacuum under the action of two gauges different of an electromagnetic field and in NC phase space coordinates, by using Schwinger's method. As an application, all special cases of (θ,η,E,B) have studied and discussed. In addition, the influence of one and two orthogonal plane wave fields on the pair creation process in Graphene is examined. The essential result of this work is that the noncommutativity has an influence on the process of pair creation from the vacuum and the plane wave not contributes to this process. Furthermore, we have solved the Dirac-Graphene equation for quasiparticles in interaction with the combination of a plane wave and a parallel magnetic field, following two different techniques. The first one is by using the Redmond method and the second is the Delta functional method. We have studied also the pair creation of Graphene's quasiparticle-hole from the vacuum by this configuration of the field.
