PROBLEMS OF GAUGE INVARIANCE IN COMPOSITE-PARTICLE THEORY

Ordinarily, a one-particle state in conventional field theory is said to be composite if Z1=0, Z2=0. (Z1 and Z2 are the usual vertex and wave-function renormalization constants.) The presence of neutral vector bosons coupled to a conserved current complicates the issues in two related aspects: (1) Z1 and Z2 become gauge-dependent, so that any equation like Z2=0 is suspect, since the notion of compositeness should be gauge-invariant; (2) there is a theory (spinor-vector scattering) in which the spinor particle is automatically Reggeized, while one ordinarily expects only composite particles to lie on Regge trajectories. In this paper, we show that the notion of compositeness is indeed gauge-invariant. Further, we show that, in spinor-vector scattering, one may pick a special gauge in which the spinor shows some of the properties of a composite particle, and in which all manifestly non-Reggeized terms in the scattering amplitude vanish. Of course, the scattering amplitude is gauge-invariant, so there were no non-Regge terms to begin with. © 1969 The American Physical Society.