Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory

Abstract

We develop a system of equations for the propagators and three point functions of the ${\varphi }^3$ 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.

arXiv comment22 pages, tikZ figures. v3: Precisions added from suggestions of the referees. v2: some clarifications in section 1.3

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Cited by in corpus (6)

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• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Remarks on a melonic field theory with cubic interaction
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Ladders and rainbows in Minimal Subtraction