Topological Methods in Geometric Foundations of Teleparallel Fused Quantum Gravity

Abstract

We have studied the gravitation in the context of the noncommutative manifold M₄×Z₂ where Z₂ is not the two point space but corresponds to a direction-vector attached to a space-time point. A local field theory, noncommutative Yang - Mills fields is limited to obtain the return thatsuch a symmetry group differences are. Noncommutative gauge symmetry of space - time and theinternal symmetry of the mixer is a very natural and clear perception that the gravitational forcegauge a characteristic feature of the theory. The gauge fields of the dimensionally reduced noncommutativeYang-Mills theory map onto a Weitzenbӧck spacetime and a teleparallel theory of gravity arisesas the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartanspace-time characterized by connections with both nonvanishing torsion and curvature. This analysissuggests that noncommutative Yang-Mills theory naturally induces gravitation through a torsioned space-time. Thus as in the case of a noncommutative manifold whereZ₂ is a two-point space there appears to be aconnection between gravity and electroweak theory in this formalism this is achieved through therealization of chiral anomaly and torsion. It is noted to be that that Weitzenbӧck geometry thatEinstein's General Relativity with the teleparallel gravity equivalent, provoked by her some notablefeatures are. This show has been that the geometry torsioned space-time at which the the chiralanomaly inconsistencies in the torch made is. This show is that it naturally Weitzenbӧck geometryof the moves that the gravity of a teleparallel formula birth towards.