Light Spin - One Particles Imply Gauge Invariance

Recently, calculations which consider the implications of anomalous trilinear gauge-boson couplings, both at tree-level and in loop-induced processes, have been criticized on the grounds that the lagrangians employed are not SU L (2) × U Y (1)gauge invariant. We prove that, in fact, the general Lorentz-invariant and U (1) em invariant but not SU L (2) × U Y (1) invariant action is equivalent to the general lagrangian in which SU L (2) × U Y (1) appears but is nonlinearly realized. We demonstrate this equivalence in an explicit calculation, and show how it is reconciled with loop calculations in which the different formulations can (superficially) appear to give different answers. In this sense any effective theory containing light spin-one particles is seen to be automatically gauge invariant.