Non-uniqueness of quantized Yang - Mills theories

Abstract

We consider quantized Yang - Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant to first order contains a two-parametric ambiguity in the ghost sector: a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are also gauge invariant. Moreover, we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of the divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the simplest one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proved for all orders.