skip to main content

The generalized representation of Dirac equation in two dimensions



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 2×2 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, (iγμ∂μ −m) 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.

Graphical Abstract