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Record W2044999237 · doi:10.1063/1.1521522

Spin networks for noncompact groups

2003· article· en· W2044999237 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of Mathematical Physics · 2003
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsPerimeter Institute
Fundersnot available
KeywordsInvariant (physics)Hilbert spaceBRST quantizationQuotientGauge groupIntroduction to gauge theorySpin networkGauge theoryHamiltonian lattice gauge theoryObservable

Abstract

fetched live from OpenAlex

Spin networks are a natural generalization of Wilson loop functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge groups is enough for the study of Yang–Mills theories, however it is well known that noncompact groups naturally arise as internal gauge groups for Lorentzian gravity models. In this context, a proper construction of gauge invariant observables is needed. The purpose of the present work is to define the notion of spin network states for noncompact groups. We first build, by a careful gauge fixing procedure, a natural measure and a Hilbert space structure on the space of gauge invariant graph connections. Spin networks are then defined as generalized eigenvectors of a complete set of hermitic commuting operators. We show how the delicate issue of taking the quotient of a space by noncompact groups can be address in term of algebraic geometry. We finally construct the full Hilbert space containing all spin network states. Having in mind applications to gravity, we illustrate our results for the groups SL(2,R) and SL(2,C).

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.611
Threshold uncertainty score0.604

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.071
GPT teacher head0.391
Teacher spread0.320 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it