Recursive Graphical Construction for Feynman Diagrams and Their Weights in Ginzburg-Landau Theory

TL;DR

This paper develops a recursive graphical method to systematically construct and compute weights of Feynman diagrams in the Ginzburg-Landau theory, up to four loops, enhancing understanding of the theory's vacuum structure.

Contribution

It introduces a recursive graphical approach to generate and evaluate Feynman diagrams and their weights in Ginzburg-Landau theory, up to four loops, providing a new systematic computational tool.

Findings

Constructed all connected vacuum diagrams up to four loops.

Derived weights for each diagram using the recursion relation.

Provided a systematic graphical method for higher-order calculations.

Abstract

The free energy of the Ginzburg-Landau theory satisfies a nonlinear functional differential equation which is turned into a recursion relation. The latter is solved graphically order by order in the loop expansion to find all connected vacuum diagrams, and their corresponding weights. In this way we determine the connected vacuum diagrams and their weights up to four loops.