Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity

Understand

General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper.

• Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the noncommutativity algebra of the coordinates in the canonical case of noncommutative geometry, this idea is closely related to noncommutative geometry as well as to canonical quantization of gravity.
• According to this presupposition generalized field equations for general relativity are derived which are obtained by replacing the usual tetrad field by the tetrad field operator within the actions and then building expectation values of the corresponding field equations between coherent states.
• These coherent states refer to creation and annihilation operators created from the components of the tetrad field operator.