Eur. Phys. J. Plus (2012) 127: 121
https://doi.org/10.1140/epjp/i2012-12121-0

Regular Article

Generalized Fierz identities and applications to spin-3/2 particles

¹ School of Physics, Nankai University, 300071, Tianjin, China
² College of Science, Tianjin University of Technology, 300384, Tianjin, China

Received: 4 July 2012
Revised: 9 August 2012
Accepted: 5 September 2012
Published online: 4 October 2012

Abstract

We study the most general Fierz identities for a pair of non-contracted Dirac matrices both in the standard basis and for chiral spinors. These identities are useful in building independent effective operators of fermions that involve derivatives or sextuple and more fields. We apply them to construct independent effective four-fermion interactions that contain one to three spin-3/2 chiral fields. These operators could be relevant to physics of higher-spin baryons and phenomenology of a neutral, massive spin-3/2 particle as a dark-matter candidate.