Functional perturbative approach to equal-time correlation functions

Abstract

Equal-time correlation functions play a central role in the recent noncovariant approaches to infrared QCD in the Coulomb gauge. In this article, we explore the possibilities to derive equal-time correlation functions from a generating functional, represent them diagrammatically, and formulate nonperturbative relations similar to Dyson–Schwinger equations among them, in analogy to the covariant n-point functions. For simplicity, we set up the formalism for λϕ4 theory and derive explicit expressions for the equal-time 2- and 4-point functions.