Canonical quantization of two-dimensional gravity with torsion and the problem of time

Schaller, P.; Strobl, Thomas

doi:10.1088/0264-9381/11/2/006

Cited by 44 publications

(72 citation statements)

References 21 publications

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“…With a temporal gauge fixing for the Cartan variables also used in the quantized theory, the geometric part of the action yields the exact path integral. Possible background geometries appear naturally as homogeneous solutions of differential equations which coincide with the classical ones, reflecting "local quantum triviality" of 2D gravity theories in the absence of matter, a property which had been observed as well before in the Dirac quantization of the KV-model [377].…”

Section: Introductionmentioning

confidence: 67%

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Dilaton gravity in two dimensions

2002

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The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important examples of spherically symmetric Black Holes, together with string inspired models, belong to this class, valuable knowledge can also be gained for these systems in the quantum case. In the last decade new insights regarding the exact quantization of the geometric part of such theories have been obtained. They allow a systematic quantum field theoretical treatment, also in interactions with matter, without explicit introduction of a specific classical background geometry. The present review tries to assemble these results in a coherent manner, putting them at the same time into the perspective of the quite large literature on this subject.

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Section: Introductionmentioning

confidence: 67%

“…This is true in SRG, but e.g. in the KV-model [250] such a "point-solution" may appear for certain values of the parameters [377]. If X + = 0 the first component of eq.…”

Section: All Classical Solutionsmentioning

confidence: 94%

Dilaton gravity in two dimensions

2002

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“…First the quadratic model was solved in the conformal [9,10] and light-cone [12] gauge. In [13,14,15] a solution for the quadratic model was in fact obtained without gauge fixing. Afterwards this solution was clarified and generalized in the papers [37,19].…”

Section: A General Solution Without Mattermentioning

confidence: 99%

“…In this way constant curvature gravity models are included in two-dimensional gravity with torsion with a well defined purely geometric action and a natural way of introduction of matter fields. The equations of motions of two-dimensional gravity with torsion were integrated in the light-cone gauge [12] and without any gauge fixing [13,14,15]. At that time the equivalence of two-dimensional gravity with torsion and dilaton gravity was unknown, and solution of the equations of motion for a generalized dilaton gravity was independently obtained in the light-cone gauge [16].…”

Section: Introductionmentioning

confidence: 99%

Effective Action for Scalar Fields in Two-Dimensional Gravity

Katanaev

2002

Annals of Physics

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We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.

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“…Much of the recent progress [7,[15][16][17][18] to understand bosonic gravity theories in two dimensions also at the quantum level is based upon the equivalence [19,20] of a torsion free general dilaton theory [21][22][23][24][25] and a Hamiltonian action of the type of a Poisson-Sigma model (PSM) [26,27]. A (graded) PSM ((g)PSM) is defined by the action (1.1)…”

Section: Introductionmentioning

confidence: 99%

Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

Bergamin

Kummer

2003

J. High Energy Phys.

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Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them -like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint-in the "genuine" supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

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Canonical quantization of two-dimensional gravity with torsion and the problem of time

Cited by 44 publications

References 21 publications

Dilaton gravity in two dimensions

Dilaton gravity in two dimensions

Effective Action for Scalar Fields in Two-Dimensional Gravity

Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

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