## Covariant basis induced by parity for the \$(j,0)\oplus (0,j)\$ representation    [PDF]

Selim Gómez-Ávila, M. Napsuciale
In this work, we build a covariant basis for operators acting on the \$(j,0)\oplus(0,j)\$ Lorentz group representations. The construction is based on an analysis of the covariant properties of the parity operator, which for these representations transforms as the completely temporal component of a symmetrical tensor of rank \$2j\$. The covariant properties of parity involve the Jordan algebra of anti commutators of the Lorentz group generators which unlike the Lie algebra is not universal. We make the construction explicit for \$j=1/2,1\$ and 3/2, reproducing well-known results for the \$j=1/2\$ case. We provide an algorithm for the corresponding calculations for arbitrary \$j\$. This covariant basis provides an inventory of all the possible interaction terms for gauge and non-gauge theories of fields for these representations. In particular, it supplies a single second rank antisymmetric structure, which in the Poincar\'e projector formalism implies a single Pauli term arising from gauge interactions and a single (free) parameter \$g\$, the gyromagnetic factor, which characterizes all multipoles of these fields regardless of the spin value.
View original: http://arxiv.org/abs/1307.4711