A local true Hamiltonian for the CGHS model in new variables

Saeed Rastgoo

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A local true Hamiltonian for the CGHS model in new variables

Saeed Rastgoo

General Relativity and Quantum Cosmology · Submitted 30 Apr 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.91 · mentions code or data availability 0.02.

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Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given. We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a generic class of two dimensional dilatonic gravitational systems coupled to matter. This gives us a second class system, a total Hamiltonian consisting of a Hamiltonian constraint, a diffeomorphism constraint and two second class constraints. We calculate the Dirac brackets, bring them to a standard form similar to the Poisson brackets by introducing a new variable. Then by rescaling lapse and shift, the Hamiltonian constraint is transformed into a form where it has an strong Abelian algebra with itself. This property holds both in vacuum case and in case with matter coupling. Then for each of the vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set for each case, and solve the classical system completely in both cases. The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian. We also show that our formalism is consistent with the original CGHS paper by showing that the equations of motion are the same in both cases. Finally we derive the relevant surface term of the model.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given.	contribution 0.77	0.91	0.34	asserted 1.00
s1	We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a generic class of two dimensional dilatonic gravitational systems coupled to matter.	method 0.93	0.93	0.06	asserted 1.00
s2	This gives us a second class system, a total Hamiltonian consisting of a Hamiltonian constraint, a diffeomorphism constraint and two second class constraints.	result 0.77	0.90	0.08	asserted 1.00
s3	We calculate the Dirac brackets, bring them to a standard form similar to the Poisson brackets by introducing a new variable.	method 0.98	0.96	0.06	asserted 1.00
s4	Then by rescaling lapse and shift, the Hamiltonian constraint is transformed into a form where it has an strong Abelian algebra with itself.	method 0.65	0.94	0.10	asserted 1.00
s5	This property holds both in vacuum case and in case with matter coupling.	result 0.99	0.81	0.07	asserted 1.00
s6	Then for each of the vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set for each case, and solve the classical system completely in both cases.	method 0.60	0.95	0.16	asserted 1.00
s7	The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian.	method 0.53	0.96	0.57	asserted 1.00
s8	We also show that our formalism is consistent with the original CGHS paper by showing that the equations of motion are the same in both cases.	result 0.78	0.93	0.09	asserted 0.94
s9	Finally we derive the relevant surface term of the model.	result 0.73	0.97	0.07	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given. We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a generic class of two dimensional dilatonic gravitational systems coupled to matter. This gives us a second class system, a total Hamiltonian consisting of a Hamiltonian constraint, a diffeomorphism constraint and two second class constraints. We calculate the Dirac brackets, bring them to a standard form similar to the Poisson brackets by introducing a new variable. Then by rescaling lapse and shift, the Hamiltonian constraint is transformed into a form where it has an strong Abelian algebra with itself. This property holds both in vacuum case and in case with matter coupling. Then for each of the vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set for each case, and solve the classical system completely in both cases. The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian. We also show that our formalism is consistent with the original CGHS paper by showing that the equations of motion are the same in both cases. Finally we derive the relevant surface term of the model.

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9 arXiv papers cite this in 16 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Uses its method or tool 1 paper

Furthermore, based on a proposal in Refs. [ref] , a redefinition of the scalar constraint is made, such that this constraint admits the standard algebra with the diffeomorphism constraint, while having a vanishing brackets with itself.

Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution · Introduction · 0.88

Cites it as background 6 papers

To start, we shall remind the reader that the most general diffeomorphism invariant action yielding second order differential equations for the metric $g_ab$ and a scalar (dilaton) field $Φ$ in two dimensions coupled to a scalar matter field $f$, is [ref] [equation] where $g=(g_ab)$ and $Y(Φ), V((∇Φ)^2,Φ)$ and $W(Φ)$ are model dependent functions of the dilaton field [ref] .

Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model · General 2D dilaton theories · 0.93
In LQG, there have been numerous works studying both the interior and the full spacetime of the Schwarzschild black hole [ref] .

Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP · Introduction · 0.96
In Loop Quantum Gravity (LQG) [ref] which is one of the main nonperturbative approaches to the quantization of gravity, there has been numerous studies of both the interior and the full spacetime of black holes in four and lower dimensions [ref] .

Deformed algebra and the effective dynamics of the interior of black holes · Introduction · 1.00

What it cites · 10 sentences without a confident label

Uses the method or tool of 1 paper

In more precise way we have [equation] which means that the shift vanishes, [equation] Now, from ([ref]), ([ref]) and ([ref]), the partially gauge fixed total Hamiltonian will become [equation] For the second gauge fixing, we follow the procedure suggested in [ref] .

Spherically symmetric gravity coupled to a scalar field with a local Hamiltonian: the complete initial-boundary value problem using metric variables · Gauge fixing the case coupled to matter · 0.88

Compares with 1 paper

Now if we use these transformations in ([ref]), the form of $E^x$ will becomes exactly the same as the form it gets in the vacuum case in the conformal gauge in [ref] .

Evanescent Black Holes · Gauge fixing the vacuum theory · 0.87

Cites as background 9 papers

The two dimensional gravitational systems with black hole solutions, specially the CGHS model [ref] , have proven to be a very good test bench to try out various ideas about quantum gravity.

Evanescent Black Holes · Introduction · 1.00
There is an extensive study of these systems in the literature (for a short list of references see [ref] and the references within them) and there have been numerous attempts to understand some quantum phenomena, such as black hole evaporation, information loss and the asymptotic fate of spacetime, using their black hole solutions.

Dirac Quantization of Two-Dimensional Dilaton Gravity Minimally Coupled to N Massless Scalar Fields · Introduction · 1.00
There is an extensive study of these systems in the literature (for a short list of references see [ref] and the references within them) and there have been numerous attempts to understand some quantum phenomena, such as black hole evaporation, information loss and the asymptotic fate of spacetime, using their black hole solutions.

Evaporation of 2-Dimensional Black Holes · Introduction · 1.00

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