Simple derivation of general Fierz-type identities

Abstract

General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex $4\times 4$ matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning.

9pages. Few sentences modified in introduction and in conclusion. Typos corrected. An example added in introduction. Title modified