Harmonic gauge in canonical gravity

Kuchař, Karel; Torre, Charles G

doi:10.1103/physrevd.44.3116

Cited by 78 publications

(152 citation statements)

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“…Such 'reference fluids' [5] have been used recently to attempt to solve the problem of time in quantum gravity. In this approach coordinate conditions are chosen in the action via lagrange multipliers thereby breaking diffeomorphism invariance, and then the theory is re-parametrized to restore this invariance.…”

Section: Discussionmentioning

confidence: 99%

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General covariance, loops, and matter

Husain

1993

Phys. Rev. D

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A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields.The theory has an infinite number of physical observables (or constants of the motion) which are constructed from loops made from scalar field configurations. The Poisson algebra of these observables is closed and is the same as that for the 3+1 gravity loop variables in the Ashtekar formalism. The theory also has observables that give the areas of open surfaces and the volumes of finite regions.Solutions to all the Hamilton-Jacobi equations for the theory and the Dirac quantization conditions in the coordinate representation are given. These solutions are holonomies based on matter loops. A brief discussion of the loop space representation for the quantum theory is also given together with some implications for the quantization of 3+1 gravity.

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Section: Discussionmentioning

confidence: 99%

“…For the case of pure (spatially closed) gravity, no such observables are known but there are indications that inclusion of matter to define reference systems may help to determine physical observables [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

General covariance, loops, and matter

Husain

1993

Phys. Rev. D

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“…This fact proves that the gauge invariance needs to be broken (at least in part) in some suitable natural way, perhaps by adding a mass term or Lagrange mulipliers [61]A satisfactory causality principle would judge an entire theory (including any gauge fixing and positivity conditions), not merely individual solutions, as physically acceptable or not, pace Logunov et al…”

Section: Dueling Null Cones?mentioning

confidence: 99%

“…This quantity has often appeared to be the preferred variable, not only in flat spacetime forms of general relativity (e.g., [5,6]), but also in other contexts. The DeDonder gauge condition, also known as the harmonic coordinate condition, prefers this variable [60,61]; the desirability of this gauge was strongly urged by Fock. More recently, A. Anderson and J. York have found the "slicing density" [62], a weight −1 densitized version of the ADM lapse, to be quite useful.…”

Section: Full Universally-coupled Actionmentioning

confidence: 99%

Slightly Bimetric Gravitation

Pitts

Schieve

2001

General Relativity and Gravitation

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The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance.Next we slightly weaken the assumptions of universal coupling and gauge invariance, obtaining a larger "slightly bimetric" class of theories, in which the Euler-Lagrange equations depend only on a curved metric, matter fields, and the determinant of the flat metric. The theories are equivalent to generally covariant theories with an arbitrary cosmological constant and an arbitrarily coupled scalar field, which can serve as an inflaton or dark matter.The question of the consistency of the null cone structures of the two metrics is addressed.

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“…Kastrup and Thiemann [1] and Kuchař [2,3,4] have pioneered the technique of midisuperspace quantization, a canonical quantization of a gravitational system with symmetries, and yet possessing infinitely many degrees of freedom. A prime example of this is the canonical quantization of the Schwarzschild geometry associated with an eternal black hole [3].…”

Section: Introductionmentioning

confidence: 99%