Adjointness Relations as a Criterion for Choosing an Inner Product

Alan D. Rendall

RECORD

Adjointness Relations as a Criterion for Choosing an Inner Product

Alan D. Rendall

General Relativity and Quantum Cosmology · Submitted 1 Mar 1994

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

The authors' main claim An erroneous claim in a previous paper is corrected and a cautionary example is presented.

how it is stated · asserted 0.97 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, 2,865 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.44 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.66 · 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.

This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.

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	This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich.	background 0.85	0.16	0.02	asserted 0.97
s1	Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed.	contribution 0.53	0.18	0.10	asserted 0.68
s2	An erroneous claim in a previous paper is corrected and a cautionary example is presented.	contribution 0.96	0.85	0.31	asserted 0.97

What kind of paper the classifier reports this is: position or commentary 0.99 · evidence from argument 0.58.

What was examined, and what was not

sources read

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

This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.

Human review

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References

Forward citations

Cited by 3 Pith papers

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

Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
hep-th 2000-05 conditional novelty 6.0 of 10

Heat-kernel coherent states on a graph are shown to be Gaussian-peaked at a phase-space point whose complexified connection is an explicit polar decomposition of the real connection and electric flux, with the Heisenb...
Gauge Field Theory Coherent States (GCS) : I. General Properties
hep-th 2000-05 conditional novelty 6.0 of 10

A heat-kernel complexifier gives an explicit, background-independent map from real connection and electric-field variables to the complexified holonomy that labels a coherent state.
Introduction to Loop Quantum Cosmology
gr-qc 2011-09 accept novelty 2.0 of 10

A structured survey of loop quantum cosmology reporting that minisuperspace models replace the big bang with a bounce, while midisuperspace and effective-dynamics work remains incomplete.

How the literature uses it

2 arXiv papers cite this in 2 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 · 1 sentence without a confident label

Uses its method or tool 1 paper

Thanks to this fact, one can characterize the physical Hilbert space as the Hilbert space of such initial data, with an inner product that can be determined by imposing reality conditions on a complete set of observables [ref] .

Hybrid Loop Quantum Cosmology: An Overview · Hybrid LQC: The Gowdy model · 0.80

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