RECORD
The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance
General Relativity and Quantum Cosmology · Submitted 24 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us.
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
The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non- degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non- degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re- derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. | background 0.99 | 0.13 | 0.05 | asserted 1.00 |
| s1 | This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. | background 0.93 | 0.05 | 0.03 | asserted 0.87 |
| s2 | Koslowski generalised the LQG representation so as to describe states labelled by smooth non- degenerate triad fields. | background 1.00 | 0.04 | 0.06 | asserted 1.00 |
| s3 | His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. | background 1.00 | 0.05 | 0.04 | asserted 1.00 |
| s4 | Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non- degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. | contribution 0.97 | 0.75 | 0.10 | asserted 0.92 |
| s5 | In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. | method 0.74 | 0.84 | 0.11 | asserted 1.00 |
| s6 | Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. | contribution 0.54 | 0.69 | 0.06 | asserted 0.99 |
| s7 | Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. | method 0.74 | 0.34 | 0.04 | asserted 1.00 |
| s8 | As a by product, we re- derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification. | result 0.89 | 0.95 | 0.16 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- 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
The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non- degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non- degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re- derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.
Human review
How the literature uses it
6 arXiv papers cite this in 37 sentences
Papers citing it · 32 sentences without a confident label
Builds on it 1 paper
-
Accordingly, building on the work of Koslowski and Sahlmann, we initiated a study of the KS representation in References [ref] .
The Koslowski-Sahlmann representation: Quantum Configuration Space · Introduction · 0.83
Uses its method or tool 2 papers
-
We now use the KS representation of $$ (see section [ref] and [ref] ) to construct a positive linear functional (PLF) on $$.
The Koslowski-Sahlmann representation: Quantum Configuration Space · Realization of the KS Hilbert space as the space $L^2(,)$ · 0.81
-
We start with the candidate for a group averaging map as in [ref] : η(|ψ|)⟩= { [ 0 if _ψ ⊊_ψ; ; η_[ψ]∑_∈̧/_ψ (U(a_) |ψ|)⟩^† if _ψ = _ψ , ] .
A quantum kinematics for asymptotically flat spacetimes · Setup · 0.97
Compares with it 1 paper
-
This representation is related to the pure background representation of [ref] , but with the roles of position and momentum reversed.
Loop quantum gravity coupled to a scalar field · The Ashtekar-Barbero connection position representation and the BF vacuum · 1.00
What it cites · 16 sentences without a confident label
Contests 1 paper
-
It is pertinent to note that in the case of generic triads of rank 2,3 there are no internal rotations which preserve the triad so that the argument of the previous paragraph cannot be applied to this case [This was not realised in the pioneering work of Reference [ref] . ].
On loop quantum gravity kinematics with non-degenerate spatial background · On the restriction to gauge invariant spin nets. · contest 0.88
Cites as background 5 papers
-
This includes:(a) the definition of classical holonomy, flux and background exponential functions, (b) their transformations under the gauge transformations generated by the classical $SU(2)$ Gauss Law and spatial diffeomorphism constraints of gravity, (c) a demonstration [ref] that the KS Hilbert space provides a representation for the operator correspondents of the functions in (a) as well a unitary representation of the transformations of (b).
The generator of spatial diffeomorphisms in the Koslowski- Sahlmann representation · Introduction · 0.88
-
The gauge symmetry group will be referred to as the bundle automorphism group [ref] or, in short, as the automorphism group.
On loop quantum gravity kinematics with non-degenerate spatial background · Preliminaries · 0.82
-
Recently Sengupta analyzed the quantization of PFT in a KS-like representation [ref] .
Quantum geometry with a nondegenerate vacuum: a toy model · Avenues for further work · 0.85
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.