Question

What is the significance of gamma 5 matrix in dirac formalism?

Answer 1

In mathematical physics, the gamma matrices, {\displaystyle \{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\}}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutationrelations that ensure they generate a matrix representation of the Clifford algebra Cℓ1,3(R). It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.

In Dirac representation, the four contravariantgamma matrices are