# Renormalized Quantum Yang-Mills Fields in Curved Spacetime

@article{Hollands2007RenormalizedQY, title={Renormalized Quantum Yang-Mills Fields in Curved Spacetime}, author={Stefan Hollands}, journal={Reviews in Mathematical Physics}, year={2007}, volume={20}, pages={1033-1172} }

We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its…

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