Expansion in Feynman Graphs as Simplicial String Theory

TL;DR

This paper establishes a direct correspondence between the series expansion of quantum field theory via Feynman diagrams and the partition function of simplicial string theory, linking quantum fields to geometric embeddings.

Contribution

It explicitly maps Feynman diagram expansions to simplicial string theory partition functions, providing a geometric interpretation of quantum field theory.

Findings

Feynman diagrams correspond to two-dimensional simplicial complexes.

Summation over geometries arises from Feynman diagram summation and Schwinger parameter integration.

Derived a one-dimensional analog using the free relativistic particle.

Abstract

We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial complexes into the space--time of the field theory. The summation over two--dimensional geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the one--dimensional analog of the simplicial theory on the example of the free relativistic particle.