Ward-Schwinger-Dyson equations in $\phi^3_6$ Quantum Field Theory

TL;DR

This paper formulates a renormalized system of Ward-Schwinger-Dyson equations for six-dimensional $\,\phi^3$ quantum field theory, enabling analysis of propagators and three-point functions with potential applications to gauge fields.

Contribution

It introduces a novel, purely renormalized formulation of Ward-Schwinger-Dyson equations in six-dimensional $\,\phi^3$ theory, incorporating renormalization group equations for better solution analysis.

Findings

System of equations formulated in terms of renormalized quantities

Solutions satisfy renormalization group equations

Potential for generalization to gauge field theories

Abstract

We develop a system of equations for the propagators and three point functions of the $\phi^3$ quantum field theory in six dimensions. Inspired from a refinement by Ward on the Schwinger--Dyson equations, the main characteristics of this system are to be formulated purely in terms of renormalized quantities and to give solutions satisfying renormalisation group equations. These properties were difficult to get together, due to the overlapping divergences in the propagator. The renormalisation group equations are an integral part of any efficient resolution scheme of this system and will be instrumental in the study of the resurgent properties of the solutions. It is our belief that this method can be generalized to the case of gauge fields, shedding some light on their quantum properties.