RECORD
Quantum Observables and Recollapsing Dynamics
General Relativity and Quantum Cosmology · Submitted 27 Apr 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse.
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.
Open the compiled record
The abstract, sentence by sentence
Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test cases. Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. | contribution 0.48 | 0.70 | 0.15 | hedged possibility 1.00 |
| s1 | This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test cases. | result 0.91 | 0.93 | 0.12 | asserted 1.00 |
| s2 | Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse. | result 0.88 | 0.91 | 0.68 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v5
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test cases. Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse.
Human review
References
How the literature uses it
20 arXiv papers cite this in 42 sentences
Papers citing it · 27 sentences without a confident label
Uses its method or tool 2 papers
-
Fortunately, however, one may use the standard Fock space (which we call the `auxiliary' Hilbert space $$) to build a new `physical' Hilbert space $$ of de Sitter-invariant states via group averaging [ref] [See [ref] for independent introductions of similar techniques in related contexts.].
Group Averaging of massless scalar fields in 1+1 de Sitter · Introduction · 0.85
-
In order to do that, we can follow two alternative strategies: =0pt * We can apply the group averaging procedure [ref] .
Introduction to Loop Quantum Cosmology · Physical Hilbert space · 0.92
Cites it as background 11 papers
-
The issues involved are very similar to those that arise in Dirac quantization of constrained systems [ref] ; indeed, group-averaging was independently introduced in that context [ref] .
Group Averaging for de Sitter free fields · Introduction · 0.93
-
See [ref] for studies of these observables in various models.
Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables · Relational Observables and the Physical Hilbert space · 0.90
-
Such gauge invariant operator typically takes the form of the `relational observable', which is obtained by localizing the operator in relation to some background states playing the role of the clock and the rod [ref] (see [ref] for earlier discussions and also [ref] ).
Implication of dressed form of relational observable on von Neumann algebra · Introduction · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.