Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

Ashtekar, Abhay; Lewandowski, Jerzy; Marolf, Donald; Mourão, José M.; Thiemann, Thomas

doi:10.1063/1.531252

Cited by 561 publications

(1,429 citation statements)

References 45 publications

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“…Note 3 This is akin to the sum over the uncountable label set of graphs in LQG [8]. Just as the set of spin network states organise themselves into a seperable set of states associated with each graph label, here we have a seperable Fock space associated with each embedding label.…”

Section: ) 4 It Can Easily Be Verified With These Definitions Thatxmentioning

confidence: 99%

“…From our previous work [5], we anticipate (for n > 1) that there are obstacles to definê C A (x) as operators. Therefore, motivated by the treatment of the quantum (spatial diffeomorphism) constraints in LQG [8], we adopt the following strategy which focuses on the finite canonical transformations generated by C A (x) rather than on C A (x) itself.…”

Section: Problems Withĥ G and Their Resolution In Terms Of A Treatmentioning

confidence: 99%

“…In this work, we show that these apprehensions are unjustified by constructing a Dirac quantization of PFT (in any spacetime dimension) which is unitarily equivalent to the standard Fock quantization. Our construction makes vital use of techniques developed in LQG (see [8] and references therein). Indeed, in the absence of these techniques, this work would not have been possible.…”

Section: Introductionmentioning

confidence: 99%

“…It provides an anomaly free, unitary representation for a certain generalization of the finite (as opposed to infinitesmal) transformations generated by the constraints. Using Group Averaging techniques from LQG [8,9] one can construct physical states from kinematic ones. The physical Hilbert space, H phys , contains those states which are invariant under the unitary action of the 'exponentiated' constraints and comes with a natural inner product as a result of Group Averaging.…”

Section: Introductionmentioning

confidence: 99%

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Dirac quantization of parametrized field theory

Varadarajan

2007

Phys. Rev. D

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Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the 'embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrodinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schrodinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization.We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are powerful enough to super-cede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints and group averaging techniques. The difference between the 1+1 dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory not the infinitesimal ones.

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Section: ) 4 It Can Easily Be Verified With These Definitions Thatxmentioning

confidence: 99%

Section: Problems Withĥ G and Their Resolution In Terms Of A Treatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dirac quantization of parametrized field theory

Varadarajan

2007

Phys. Rev. D

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“…It was first formulated as a general scheme in [1,9] and recently developed further in [3,4]. Here I wish to report on these recent developments.…”

Section: Introductionmentioning

confidence: 99%

Group averaging and refined algebraic quantization

Giulini

2000

Nuclear Physics B - Proceedings Supplements

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Chiral supergravity and anomalies

Mielke

Macı́as

1999

Ann. Phys.

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Similarly as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.Recent developments by Ashtekar [1,2], constitute considerable progress in the canonical formulation of general relativity and its relation to SU(2) Yang-Mills theory. The key feature of Ashtekar's formulation of general relativity *

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Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

Cited by 561 publications

References 45 publications

Dirac quantization of parametrized field theory

Dirac quantization of parametrized field theory

Group averaging and refined algebraic quantization

Chiral supergravity and anomalies

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