INTERSECTION OF YANG–MILLS THEORY WITH GAUGE DESCRIPTION OF GENERAL RELATIVITY

Abstract

An intersection of Yang–Mills theory with the gauge description of general relativity is considered. This intersection has its origin in a generalized algebra, where the generators of the SO(3, 1) group as gauge group of general relativity and the generators of a SU(N) group as gauge group of Yang–Mills theory are not separated anymore but are related by fulfilling nontrivial commutation relations with each other. Because of the Coleman–Mandula theorem this algebra cannot be postulated as Lie algebra. As consequence, extended gauge transformations as well as an extended expression for the field strength tensor is obtained, which contains a term consisting of products of the Yang–Mills connection and the connection of general relativity. Accordingly a new gauge invariant action incorporating the additional term of the generalized field strength tensor is built, which depends of course on the corresponding tensor determining the additional intersection commutation relations. This means that the theory describes a decisively modified interaction structure between the Yang–Mills gauge field and the gravitational field leading to a violation of the equivalence principle.