Axiomatic de Sitter quantum Yang-Mills theory with color confinement and mass gap

APC, UMR 7164, Université Paris Cité - 75205 Paris, France

^(a) E-mail: takook@apc.in2p3.fr (corresponding author)

Received: 15 December 2022
Accepted: 6 January 2023

Abstract

The analyticity property of de Sitter's quantum Yang-Mills theory in the framework of Krein space quantization, including quantum metric fluctuation, is demonstrated. This property completes our previous work regarding quantum Yang-Mills theory in de Sitter's ambient space formalism, and we can construct an axiomatic quantum field theory similar to Wightman's axioms. The color confinement is proven for the general case, which was previously approved in the early universe. It is shown by using the interaction between gluon fields and the conformal sector of the gravitational field, which is a massless minimally coupled scalar gauge field. The gluon mass results from the interaction between the gluon fields and the massless minimally coupled scalar field as a conformal sector of the gravitational field and then the symmetry-breaking setting due to the vacuum expectation value of the scalar field.