Axioms for Quantum Yang-Mills Theories -- 1. Euclidean Axioms

TL;DR

This paper develops a set of axioms for quantum Yang-Mills theories by extending Schwinger functions and emphasizing gauge-invariant quantities, aiming to formalize the mathematical foundation of these theories.

Contribution

It introduces a new axiomatic framework for quantum Yang-Mills theories based on gauge-invariant Schwinger functions and their physical properties.

Findings

Proposes axioms for gauge-invariant Schwinger functions

Aligns axioms with the principle that only gauge-invariant quantities are physical

Provides a foundation for rigorous mathematical formulation of Yang-Mills theories

Abstract

This paper extends the notion of Schwinger functions to quantum Yang-Mills theories and proposes the axioms they should satisfy. Two main features of this axiom scheme are that we assume existence of gauge-invariant co-located Schwinger functions and impose physical properties only on them. This is in accordance with the fundamental principle of gauge theories that only gauge-invariant quantities can be physical observables.