Gauge theory at asymptotical distance and singularity

Abstract

One of the fundamental problems of gravity to be an infinite range interaction is whether it has a gauge group via the internal structure, so that Einstein type theories couldn’t explain it yet. Gauge groups in Yang Mill type theories, i.e. weak [11] and strong [3, 8] interactions, are generally non Abelian Lie group via the Hermitian structure induced by complex valued smooth vector fields. A group labeled by U(1)⊗Ũ(d) obtained as the reduction of unitary Lie groups is presented as candidate a gauge group for each behavior at large scale and at small scale of a gauge field, in this context, integrated Einstein Yang Mills formalism on a unique geometrical frame is given. Also as seen that the (anti) self dual gauge theory of the group G = U(1) ⊗ Ũ(4) is indeed a G = U(1) theory in real 4 dimension, i.e the Maxwell theory for the electromagnetism to be an infinite range interaction. Mathematics Subject Classification: 22E15, 53C07, 53C80, 70S05, 70S15, 83C05