### Abstract

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

Original language | English (US) |
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Article number | 045043 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 92 |

Issue number | 4 |

DOIs | |

State | Published - Aug 31 2015 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*92*(4), [045043]. https://doi.org/10.1103/PhysRevD.92.045043

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 92, no. 4, 045043. https://doi.org/10.1103/PhysRevD.92.045043

**Covariance in models of loop quantum gravity : Spherical symmetry.** / Bojowald, Martin; Brahma, Suddhasattwa; Reyes, Juan D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Covariance in models of loop quantum gravity

T2 - Spherical symmetry

AU - Bojowald, Martin

AU - Brahma, Suddhasattwa

AU - Reyes, Juan D.

PY - 2015/8/31

Y1 - 2015/8/31

N2 - Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

AB - Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

UR - http://www.scopus.com/inward/record.url?scp=84940868013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940868013&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.92.045043

DO - 10.1103/PhysRevD.92.045043

M3 - Article

AN - SCOPUS:84940868013

VL - 92

JO - Physical Review D

JF - Physical Review D

SN - 0556-2821

IS - 4

M1 - 045043

ER -