Instantons in Nonirreducible Representations of the Lorentz Group

Abstract

Usually the Lorentz transformation for vector fields and spinor fields is given by $$A_\mu ^{\prime ij} (x\prime ) = \Lambda _{\mu \nu } A^{ij\nu } (x),$$ (1a) $$\psi _\alpha ^{\prime i} (x\prime ) = S_{\alpha \beta } (\Lambda )\psi _\beta ^i (x),$$ (1b) where $$S(\Lambda )\gamma _\nu S^{ - 1} (\Lambda ) = \gamma _\mu \Lambda _\nu ^\mu .$$ (2)