  In this work, the general form of $2\times2$ Dirac matrices for 2+1 dimension
is found. In order to find this general representation, all relations among the
elements of the matrices and matrices themselves 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,
$ \left( i\gamma^{\mu}\partial_{\mu}-m\right) \Psi=0 $, is consist of matrices
of even dimension known as the general representation of Dirac matrices or
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.

Quantum Physics