Constructive Renormalization for $\Phi^{4}_2$ Theory with Loop Vertex Expansion

TL;DR

This paper uses the loop vertex expansion to construct the 2D Euclidean phi^4 quantum field theory, confirming Borel summability and suggesting applicability to non-commutative models.

Contribution

It introduces a constructive approach via loop vertex expansion for phi^4_2 theory, aligning with standard results and enabling future non-commutative space-time models.

Findings

Reproduces Borel summability of Schwinger functions.

Validates the loop vertex expansion as a constructive method.

Suggests potential for non-commutative quantum field theories.

Abstract

In this paper we construct the 2 dimensional Euclidean $\phi^4$ quantum field theory using the method of loop vertex expansion. We reproduce the results of standard constructive theory, for example the Borel summability of the Schwinger functions in the coupling constant. Our method should be also suitable for the future construction of Grosse-Wulkenhaar models on non-commutative space-time.