Calculating the Fierz Transformation for Higher Orders

Abstract

We consider the higher-order Fierz transformation, which corresponds to expanding a product of $\bar{\psi }\Gamma \psi$ terms into a sum of products of Dirac densities and currents. It is shown that the Fierz transformation can be obtained by solving a large system of linear equations with fractional complex coefficients, which is practical at least up to fourth power.

Comments: 6 pages, 3 tables