Extended gauge theories in Euclidean space with higher spin fields (Q5934239)

Higher spins \((s\geq 1)\) pose severe problems in quantum field theory. The only consistent locally interacting models, so far, are gauge theories of massless particles and supersymmetric theories. Gabrielli analyzes the particle spectrum of ``extended'' Yang-Mills theories in Euclidean spacetime. In the \(\text{SU}(4)\) case, the pure sector contains the following massless particles: three spin-2, eight spin-1, and eight spin-0 particles. He also discusses the functional integral quantization of those models using a special class of covariant gauges. As a drawback he finds that matter fields can only be bosonic if they are to transform under the fundamental representation of the extended gauge group. Also, the analytic continuation to a formulation in Minkowski space has not as yet been achieved. Non-renormalizability might be linked to non-unitarity of the \(S\)-matrix and, if so, would be a physical obstacle.