The Master Ward Identity for the complex scalar field

TL;DR

This paper demonstrates that the Master Ward Identity for a complex scalar field with quartic interaction can be satisfied within a specific quantum field theory framework, ensuring symmetry preservation during renormalization.

Contribution

It establishes the validity of the Master Ward Identity for complex scalar fields with quartic interactions using deformation quantization and causal perturbation theory.

Findings

MWI can be satisfied for complex scalar fields with quartic interactions.

The proof utilizes deformation quantization and causal perturbation theory.

Examples of Ward Identities derived from the MWI are provided.

Abstract

The Master Ward Identity (MWI) gives a universal formulation of the symmetries of a classical field theory. It is a renormalization condition for the time ordered products of the corresponding quantum field theory. We show that the MWI for a complex scalar field with quartic interaction can be satisfied, with the current, the interaction and all their submonomials as allowed arguments. The proof is performed in the framework of deformation quantization combined with causal perturbation theory, which is summarized and introduced. Some examples of Ward Identities following from the proven MWI are given.