NONABELIAN GAUGE-THEORIES - THE CAUSAL APPROACH

We present the causal construction of perturbative Yang-Mills theories in four (3+1)-dimensional space-time. We work with free quantum field s throughout. The inductive causal method by Epstein and Glaser leads directly to a finite perturbation series and does not rely on an inter mediary regularization of the theory. The causal method naturally sepa rates the physical infrared problem of massless theories from ultravio let-sensitive features like normalizability by regarding the distribut ional character of the S-matrix. We prove the normalizability of the Y ang-Mills theory with fermionic matter fields and study the discrete s ymmetry transformations in the causal formalism. We introduce a defini tion of nonabelian gauge invariance which only involves the free asymp totic field operators and give mathematically rigorous and conceptuall y simple proofs of nonabelian gauge invariance and of the physical uni tarity of the S-matrix in all orders of perturbation theory. (C) 1995 Academic Press, Inc.