Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation

Steven Carlip

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Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation

Steven Carlip

General Relativity and Quantum Cosmology · Submitted 2 Sep 1993

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

The authors' main claim In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.

how it is stated · asserted 0.52 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,914 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation. In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.

background contribution method result interpretation main claim

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	In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies.	background 0.91	0.12	0.05	hedged possibility 0.82
s1	Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation.	contribution 0.56	0.53	0.06	hedged possibility 0.87
s2	In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.	result 0.98	0.85	0.83	asserted 0.52

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 0.58.

What was examined, and what was not

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arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation. In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.

Human review

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
hep-th 2004-01 conditional novelty 7.0 of 10

Gauge-fixing both symmetries of the Ponzano-Regge model yields finite transition amplitudes and a single operator formalism that unifies gauge fixing, time insertion, and the coupling of interacting spinning particles.
The spectrum of pure dS$_3$ gravity in the static patch
hep-th 2025-05 conditional novelty 6.0 of 10

The static-patch partition function of three-dimensional de Sitter gravity is identified with the future-boundary wavefunction, giving a dense discrete spectrum with negative degeneracies.

How the literature uses it

8 arXiv papers cite this in 8 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

This result demonstrates that all seemingly distinct quantum theories arising from different quantization schemes of the same classical model are fundamentally equivalent.

The exact Wheeler-DeWitt equation for the scale-factor minisuperspace model · 0.84

Papers citing it · 4 sentences without a confident label

Cites it as background 4 papers

The Wheeler–DeWitt equation ([ref]) has been studied intensively since 30 years [ref] .

Bosonic Quantum Gravity According to the Global One-Dimensionality Conjecture · Introduction: Unsolved Quantum Gravity · 0.95
Classical and quantum solutions in this dimension have been widely investigated, for instance, in [ref] .

Classical and quantum (2+1)-dimensional spatially homogeneous string cosmology · General considerations · 0.95
Classical and quantum solutions for gravity theories in this dimension have been widely investigated, for instance, in [ref] .

Regular $(2+1)$-dimensional spatially homogeneous $\alpha'$-corrected BTZ-like black hole in string theory · General considerations · 0.95

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