The generalized representation of Dirac equation intwo dimensions

Since the discovery of the dirac equation, much research has been done on the construction of various setsconsisting of dirac matrices that all of which follow the cliford algebra. but there is never notice to the relationshipbetween the internal elements of these matrices. in this work, the general form of 2×2 dirac matrices for2+1 dimension is found. in order to find this general representation, all relations among the elements of thematrices are found, and the generalized lorentz transform matrix is also found under the effect of the generalrepresentation of dirac matrices. as we know, the well known equation of dirac,􀀀iγμ∂μ −m
ψ = 0, is consist ofmatrices of even dimension known as the dirac matrices. our motivation for this study was lack of the generalrepresentation of these matrices despite the fact that more than nine decades have been passed since thediscovery of this well known equation. everyone has used a specific representation of this equation according totheir need; such as the standard representation known as dirac-pauli representation, weyl representation ormajorana representation. in this work, the general form which these matrices can have is found once for all.