Axioms for Quantum Yang-Mills Theories -- 2. Minkowski Axioms
Min Chul Lee
TL;DR
This work develops Minkowski-space axioms for quantum Yang-Mills theory, establishing two parallel schemes for describing the theory: Wightman functions and time-ordered operator products, linked through analytic continuation from Euclidean Schwinger functions. It proves that Wightman correlators can be derived from Schwinger functions at non-coincident points and that reconstructed fields yield the corresponding time-ordered products, thereby ensuring consistency between the two formalisms. The framework connects with the indefinite metric formalism and with algebraic QFT (AQFT) and BV methods, reproducing key results while clarifying the role of the underlying state-space structure. Overall, the paper provides a rigorous, gauge-covariant axiomatic foundation for non-Abelian gauge theories in Minkowski spacetime with reconstruction theorems bridging Euclidean and Minkowski formulations, enabling cross-validation across complementary frameworks.
Abstract
This paper presents the axioms for a quantum Yang-Mills theory in the Minkowski spacetime. There are two routes of analytic continuation for the Schwinger functions, namely the Wightman functions and time-ordered products of field operators. We check consistency of these two axiom schemes and reproduce some known existing results, including the indefinite metric and BV formalisms.