Loop Vertex Expansion for Phi^2k Theory in Zero Dimension

TL;DR

This paper extends the loop vertex expansion method to higher-degree interactions in zero-dimensional scalar theories, demonstrating Borel-Le Roy summability for Phi^2k theories, with explicit calculations for Phi^6.

Contribution

It introduces an extension of the loop vertex expansion to interactions beyond quartic, proving Borel-Le Roy summability for Phi^2k theories in zero dimensions.

Findings

Proves Borel-Le Roy summability of Phi^2k theories in zero dimension.

Provides explicit calculations for Phi^6 interaction.

Extends the applicability of loop vertex expansion to higher-degree interactions.

Abstract

In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of Phi^2k scalar theory in zero dimension is Borel-Le Roy summable of order k-1. We detail the computations in the case of a Phi^6 interaction.