Diagrammar In Classical Scalar Field Theory

TL;DR

This paper develops a super-diagram approach to classical scalar field theory, simplifying perturbative calculations and revealing supersymmetry that cancels many diagrams, aligning classical and quantum formalisms.

Contribution

It introduces super-diagrams and super-fields in classical scalar field theory, enabling simplified perturbative calculations up to third order and highlighting supersymmetry effects.

Findings

Super-diagrams simplify classical perturbation theory.

Supersymmetry causes cancellations among classical diagrams.

Classical perturbation theory aligns closely with quantum formalism.

Abstract

In this paper we analyze perturbatively a g phi^4 classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that several of those diagrams cancel against each other due to a universal supersymmetry present in the classical path integral mentioned above. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost "identical" formally to the quantum ones. Using the super-diagrams technique we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.