Constructive Field Theory in Zero Dimension

TL;DR

This paper reviews five different methods for computing the number of connected graphs in zero-dimensional ^4 field theory, serving as an educational overview of constructive resummation techniques.

Contribution

It provides a pedagogical summary of key methods like replica trick and forest formula for zero-dimensional ^4 field theory, without presenting new results.

Findings

Comparison of five computational methods

Clarification of constructive resummation techniques

Educational overview of zero-dimensional ^4 field theory

Abstract

In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional $\phi^4$ field theory,in increasing order of sophistication. The note does not contain any new result but may be helpful to summarize the heart of constructive resummations, namely a replica trick and a forest formula.