Renormalized Quantum Yang-Mills Fields in Curved Spacetime

Understand

We present a proof that 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 derivatives), and all their relations such as commutation relations or operator product expansion.
• It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket.