OICC Press Journal of Theoretical and Applied Physics 2251-7235 16 1 2023 11 17 The generalized representation of Dirac equation in two dimensions 10.30495/jtap.162206 EN Hamze Moayeri Physics Department, Science Faculty, Jundi-Shapur University of Technology, Dezful, Iran 0000-0001-5199-4349 Ali Chenani Physics Department, Science Faculty, Jundi-Shapur University of Technology, Dezful, Iran Alireza Hakimifard Physics Department, Science Faculty, Jundi-Shapur University of Technology, Dezful, Iran Nemat Tahmasebi Physics Department, Science Faculty, Jundi-Shapur University of Technology, Dezful, Iran 0000-0002-7214-1684 Journal Article 2023 11 17 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.