# Is there a method which quantizes non-abelian gauge theories without path integrals formalism?

In the most QFT books there is a method of quantization of non-abelian theories through path integral methods. But I want to learn also the other methods without using of this formalism. Does anyone know these methods?

Yes, one traditional alternative to the path integral formalism is the operator formalism. For QED with abelian gauge group, the old quantization formulation is the Gupta-Bleuler formulation. For QCD/Yang-Mills theory with non-abelian gauge group, the Gupta-Bleuler formulation is replaced by the BRST formulation. The BRST formulation exists in at least 3 different formalisms:

1. The Lagrangian path integral formalism.

2. The Hamiltonian path integral formalism.

3. The operator formalism.

Besides these traditional formalisms, there are also manifestly gauge invariant approaches. And there is the Wilson loop formulation by Migdal, Makeenko, and Polyakov.

Disclaimer: By the word existence, we mean at the physics level of rigor.

• Hi. Would you please recommend a good reference for 3? Thanks. – AccidentalFourierTransform Jan 2 '17 at 19:31