Inductive Approach to Loop Vertex Expansion

TL;DR

This paper introduces an inductive method for Loop Vertex Expansion, applied to $_1^4$ theory, claiming it is simpler and more natural than traditional approaches in certain contexts.

Contribution

It presents a new inductive approach to Loop Vertex Expansion, enhancing simplicity and naturalness in constructing quantum field theories.

Findings

Inductive realization of Loop Vertex Expansion demonstrated.

Applied to $_1^4$ theory with promising results.

Potential for broader applicability in quantum field theory.

Abstract

An inductive realization of Loop Vertex Expansion is proposed and is applied to the construction of the $\phi_1^4$ theory. It appears simpler and more natural than the standard one at least for some situations.