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 in 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 gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the most simple 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 proven in all orders.

22 pages. The paper is written in TEX. The necessary macros are included

References in corpus (2)

• A Causal Approach to Massive Yang-Mills Theories
• On the Algebra of Ghost Fields

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• The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
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• Quantum electrodynamics in the null-plane causal perturbation theory II
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• The Renormalization of the Non-Abelian Gauge Theories in the Causal Approach