The generalized representation of Dirac equation in two dimensions

Abstract

Since the discovery of the Dirac equation, much research has been done on the construction of various sets consisting of Dirac matrices that all of which follow the Cliford Algebra. But there is never notice to the relationship between the internal elements of these matrices. In this work, the general form of 2Ã2 Dirac matrices for 2+1 dimension is found. In order to find this general representation, all relations among the elements of the matrices are found, and the generalized Lorentz transform matrix is also found under the effect of the general representation of Dirac matrices. As we know, the well known equation of Dirac, (iγμâμ âm) Ψ = 0, is consist of matrices of even dimension known as the Dirac matrices. Our motivation for this study was lack of the general representation of these matrices despite the fact that more than nine decades have been passed since the discovery of this well known equation. Everyone has used a specific representation of this equation according to their need; such as the standard representation known as Dirac-Pauli Representation, Weyl Representation or Majorana representation. In this work, the general form which these matrices can have is found once for all.