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Exact Path Integral Quantization of Generic 2-D Dilaton Gravity
General Relativity and Quantum Cosmology · Submitted 4 Dec 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one.
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The abstract, sentence by sentence
Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Local path integral quantization of generic 2D dilaton gravity is considered. | contribution 0.77 | 0.72 | 0.04 | asserted 0.70 |
| s1 | Locality means that we assume asymptotic fall off conditions for all fields. | method 0.83 | 0.40 | 0.02 | asserted 0.98 |
| s2 | We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. | result 1.00 | 0.94 | 0.88 | asserted 1.00 |
| s3 | This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. | interpretation 0.96 | 0.52 | 0.18 | asserted 1.00 |
| s4 | For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present. | result 0.89 | 0.92 | 0.07 | asserted 0.99 |
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The paper
Original abstract
Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present.
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References
How the literature uses it
13 arXiv papers cite this in 16 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one.
Exact Path Integral Quantization of 2-D Dilaton Gravity · 1.00
Papers citing it · 11 sentences without a confident label
Uses its method or tool 2 papers
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A straightforward canonical analysis [ref] together with the Castellani algorithm [ref] yields the canonical boundary currents [ref] δQ[_I] = k/2π δX^I _I|_ρ→∞ . eq:CDV28 The key observation in deriving the result [ref] is that the secondary first class constraints contain spatial derivatives of the target space coordinates [ref] .
$AdS_2$ holography is (non-)trivial for (non-)constant dilaton · Triviality of canonical charges · 0.98
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One can find all quantum corrections by the methods developed earlier in the commutative case [ref] .
Symmetries in noncommutative field theories: Hopf versus Lie · Stability of NC Jackiw-Teitelboim model · 0.96
Cites it as background 3 papers
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See [ref] for earlier work on (semi-classical) scalar fields coupled to JT gravity.
One-loop partition function of gravity with leaky boundary conditions · Leaky boundary conditions and flux-balance laws · 0.98
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Previously in the different context the path integral for PSM and related models was also discussed in [ref] .
Poisson sigma model on the sphere · Introduction · 0.93
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For a more elaborate treatment of gauge fixing in the context of two-dimensional dilaton gravity models, the interested reader is directed to [ref] .
Ghost-free infinite-derivative dilaton gravity in two dimensions · Action and quadratic action · 0.96
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