Pith. Sign in

RECORD

Quantum Field Theory of Spin Networks

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
A. Mikovic

General Relativity and Quantum Cosmology · Submitted 27 Feb 2001

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

The authors' main claim The corresponding transition amplitude is a finite sum of Feynman diagrams, and in this way one avoids the problem of infinite amplitudes caused by summing over all possible triangulations.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDgr-qc/0102110 (version 1)
Pith IDY7DHFXY3, Pith's permanent record of this paper and its review
CitationA. Mikovic. "Quantum Field Theory of Spin Networks." arXiv:gr-qc/0102110 (2001). https://pith.science/paper/Y7DHFXY3
Claim paper

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,039 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.44 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. By promoting the group theory Fourier modes into creation and annihilation operators we construct a Fock space for the quantum field theory whose Feynman diagrams give the transition amplitudes. By making products of the Fourier modes we construct operators and states representing the spin networks associated to triangulations of spatial boundaries of a triangulated spacetime manifold. The corresponding spin network amplitudes give the state-sum amplitudes for triangulated manifolds with boundaries. We also show that one can introduce a discrete time evolution operator, where the time is given by the number of D-simplices in the triangulation, or equivalently by the number of the vertices in the Feynman diagram. The corresponding transition amplitude is a finite sum of Feynman diagrams, and in this way one avoids the problem of infinite amplitudes caused by summing over all possible triangulations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. contribution 0.94 0.91 0.08 asserted 0.98
s1 By promoting the group theory Fourier modes into creation and annihilation operators we construct a Fock space for the quantum field theory whose Feynman diagrams give the transition amplitudes. method 0.93 0.93 0.12 asserted 1.00
s2 By making products of the Fourier modes we construct operators and states representing the spin networks associated to triangulations of spatial boundaries of a triangulated spacetime manifold. method 0.80 0.91 0.10 asserted 1.00
s3 The corresponding spin network amplitudes give the state-sum amplitudes for triangulated manifolds with boundaries. result 0.90 0.80 0.30 asserted 1.00
s4 We also show that one can introduce a discrete time evolution operator, where the time is given by the number of D-simplices in the triangulation, or equivalently by the number of the vertices in the Feynman diagram. contribution 0.71 0.93 0.10 asserted 0.83
s5 The corresponding transition amplitude is a finite sum of Feynman diagrams, and in this way one avoids the problem of infinite amplitudes caused by summing over all possible triangulations. result 0.75 0.86 0.29 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from proof or derivation 1.00.

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

We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. By promoting the group theory Fourier modes into creation and annihilation operators we construct a Fock space for the quantum field theory whose Feynman diagrams give the transition amplitudes. By making products of the Fourier modes we construct operators and states representing the spin networks associated to triangulations of spatial boundaries of a triangulated spacetime manifold. The corresponding spin network amplitudes give the state-sum amplitudes for triangulated manifolds with boundaries. We also show that one can introduce a discrete time evolution operator, where the time is given by the number of D-simplices in the triangulation, or equivalently by the number of the vertices in the Feynman diagram. The corresponding transition amplitude is a finite sum of Feynman diagrams, and in this way one avoids the problem of infinite amplitudes caused by summing over all possible triangulations.

Human review

How Pith checks papers → · Full audit of this paper →

References
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

Cites it as background 1 paper
  • Fock quantization of GFT has been developed in a series of papers in Refs. [ref] (and following different approaches in [ref] and [ref] ); for a review, see [ref] .

    An Exactly Soluble Group Field Theory · Fock space for a complex GFT field · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.