NON-ABELIAN GAUGE-SYMMETRY BN THE CAUSAL EPSTEIN-GLASER APPROACH

Non-Abelian gauge symmetry in (3 + 1)-dimensional space-time is analyz ed in the causal Epstein-Glaser framework. In this formalism, the tech nical details concerning the well-known UV and IR problem in quantum f ield theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued d istributions. Non-Abelian gauge invariance in perturbation theory is c ompletely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for t he unitarity of the S matrix in the physical subspace and the usual Sl avnov-Taylor identities. We explicitly derive the most general specifi c coupling compatible wi ih this condition. By analyzing only tree gra phs in the second order of perturbation theory we show that the well-k nown Yang-Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required ge neralizations for linear gauges are given.