Spherically symmetric sector of self-dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections

Spherically symmetric sector of self-dual Ashtekar gravity coupled to matter: Anomaly-free... Using self-dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once local (pointwise) holonomy corrections are introduced, which leads to several obstructions in the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which have been suggested to be an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self-dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Spherically symmetric sector of self-dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections

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Spherically symmetric sector of self-dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections

Abstract

Using self-dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once local (pointwise) holonomy corrections are introduced, which leads to several obstructions in the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which have been suggested to be an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self-dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.026002
Publisher site
See Article on Publisher Site

Abstract

Using self-dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once local (pointwise) holonomy corrections are introduced, which leads to several obstructions in the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which have been suggested to be an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self-dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 15, 2017

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