# Infinite volume limits in Euclidean quantum field theory via stereographic projection

## TL;DR

This paper develops a general method for constructing infinite volume measures in Euclidean quantum field theory, applicable in any space-time dimension, and capable of representing scalar fields with various interactions.

## Contribution

It introduces a broad construction for infinite volume measures satisfying Euclidean QFT axioms, extending the scope to arbitrary interactions and dimensions.

## Key findings

- Constructs measures satisfying Euclidean QFT axioms in arbitrary dimensions
- Applicable to scalar fields with bounded continuous self-interactions
- Open problem: whether non-Gaussian measures are included

## Abstract

We present a general infinite volume limit construction of probability measures obeying the Glimm-Jaffe axioms of Euclidean quantum field theory in arbitrary space-time dimension. In particular, we obtain measures that may be interpreted as corresponding to scalar quantum fields with arbitrary bounded continuous self-interaction. It remains however an open problem whether this general construction contains non-Gaussian measures.