On the trace of the product of Dirac matrices occurring asA′ =A ^′ _iγi +iA ^′ ₅

Abstract

Several methods are given for evaluating the trace of the product of an arbitrary number of elementsA ^′_r which involve Dirac matrices in the manner$A'_r = A'_{r_i \gamma _i } + iA'_{r_5 }$. Formulae for the determination of expressions of the type trace$\left( {\gamma _{i_1 } \gamma _{i_2 } ...\gamma _{i_p } A'_1 A'_2 ...A'_l } \right)$ trace$\left( {\gamma _{i_1 } \gamma _{i_2 } ...\gamma _{i_p } B'_1 B'_2 ...B'_m } \right)$ are obtained. The above problems withγ ₅ also occurring in the traces are dealt with, and some useful identities involving Dirac matrices are established.