In the Hamiltonian formulation of general relativity, Einstein's equation is replaced by a set of four constraints. Classically, the constraints can be identified with the generators of the hypersurface-deformation Lie algebroid (HDA) that belongs to the groupoid of finite evolutions in space-time. Taken over to deformed general relativity, this connection allows one to study possible Drinfeld twists of space-time diffeomorphisms with Hopf-algebra techniques. After a review of noncommutative differential structures, two cases - twisted diffeomorphisms with standard action and deformed (or -) diffeomorphisms with deformed action - are considered in this paper. The HDA of twisted diffeomorphisms agrees with the classical one, while the HDA obtained from deformed diffeomorphisms is modified due to the explicit presence of -products in the brackets. The results allow one to distinguish between twisted and deformed symmetries, and they indicate that the latter should be regarded as the relevant symmetry transformations for noncommutative manifolds. The algebroid brackets maintain the same general structure regardless of space-time noncommutativity, but they still show important consequences of nonlocality.

Extending general covariance: moyal-type noncommutative manifolds / Bojowald, Martin; Brahma, Suddhasattwa; Buyukcam, Umut; Ronco, Michele. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 98:2(2018). [10.1103/PhysRevD.98.026031]

Extending general covariance: moyal-type noncommutative manifolds

Ronco, Michele
2018

Abstract

In the Hamiltonian formulation of general relativity, Einstein's equation is replaced by a set of four constraints. Classically, the constraints can be identified with the generators of the hypersurface-deformation Lie algebroid (HDA) that belongs to the groupoid of finite evolutions in space-time. Taken over to deformed general relativity, this connection allows one to study possible Drinfeld twists of space-time diffeomorphisms with Hopf-algebra techniques. After a review of noncommutative differential structures, two cases - twisted diffeomorphisms with standard action and deformed (or -) diffeomorphisms with deformed action - are considered in this paper. The HDA of twisted diffeomorphisms agrees with the classical one, while the HDA obtained from deformed diffeomorphisms is modified due to the explicit presence of -products in the brackets. The results allow one to distinguish between twisted and deformed symmetries, and they indicate that the latter should be regarded as the relevant symmetry transformations for noncommutative manifolds. The algebroid brackets maintain the same general structure regardless of space-time noncommutativity, but they still show important consequences of nonlocality.
2018
Physics and Astronomy (miscellaneous); general relativity; Einstein's equations
01 Pubblicazione su rivista::01a Articolo in rivista
Extending general covariance: moyal-type noncommutative manifolds / Bojowald, Martin; Brahma, Suddhasattwa; Buyukcam, Umut; Ronco, Michele. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 98:2(2018). [10.1103/PhysRevD.98.026031]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1227737
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