Deformation Quantization

Abstract

The reformulation of classical theory done in Chap. 3 served as a preparation for constructing QFT models. The framework that we are going to use is deformation quantization combined with causal perturbation theory. To quantize a given theory described by the action S we first need to split S into a free part S0 (at most quadratic in field configurations) and the interaction term SI. Then, we quantize the theory defined by S0, using deformation quantization based on a Moyal-type formula, and in the final step we will re-introduce the interaction using causal perturbation theory. This last step will be discussed in Chap. 6, while the present chapter deals with deformation quantization.