Quantum field theory on curved spacetimes: axiomatic framework and examples (Q2798661)

This is a very nice review article on quantum field theory on curved spacetimes. After introducing globally hyperbolic spacetimes, the authors present traditional difficulties in working on quantum field theory in such curved spacetimes. Then they explain the notion of the Haag-Kastler nets of \(C^*\)-algebras on the Minkowski space in algebraic quantum field theory, and generalize it to a locally covarinat quantum field theory on a general curved spacetime. The Weyl algebra of a free scalar field is presented as such an example.NEWLINENEWLINEThey next turn to construction of models. After working on generalized Lagrangian formalism and the Poisson structure in the classical theory, they present deformation quantization of free field theories. They next introduce interacting theories and renormalization.NEWLINENEWLINEThen study of gauge theories comes. After working out classical theory, quantization is presented.NEWLINENEWLINEThe appendix deals with mathematical tools necessary for this theory.