RECORD
Causal evolution of spin networks
General Relativity and Quantum Cosmology · Submitted 13 Feb 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.
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
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1+1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. | contribution 0.99 | 0.73 | 0.12 | asserted 0.99 |
| s1 | The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. | contribution 0.65 | 0.60 | 0.14 | asserted 1.00 |
| s2 | The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. | contribution 0.59 | 0.47 | 0.06 | hedged possibility 0.67 |
| s3 | The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. | method 0.93 | 0.63 | 0.09 | asserted 1.00 |
| s4 | The quantum dynamics thus respects the discrete causal structure of the causal sets. | result 0.43 | 0.63 | 0.16 | asserted 1.00 |
| s5 | In the 1+1 dimensional case the theory is closely related to directed percolation models. | interpretation 0.56 | 0.33 | 0.05 | asserted 0.99 |
| s6 | In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit. | interpretation 0.96 | 0.30 | 0.15 | hedged possibility 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
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1+1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.
Human review
References
How the literature uses it
11 arXiv papers cite this in 12 sentences
Papers citing it · 6 sentences without a confident label
Compares with it 1 paper
-
We note that the causality data proposed here coincide with the data proposed in the spin foam literature [ref] if one restricts to the case considered in the four-dimensional spin foam literature so-far, namely that $(i)$ all $(d-1)$-simplices are spacelike and $(ii)$ all pairs of $d$-simplices have positive relative spacetime orientation.
Causal structure and light-conical singularities in Lorentzian simplicial quantum gravity · Causality data · 1.00
Cites it as background 5 papers
-
This set in motion the development of several models [ref] which can be summarized under the collective name spin foam model.
Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity · Resolution of Identity for the Heat Kernel States in the Twisted Geometry Parametrization · 0.87
-
Soon after, Markopoulou and Smolin presented a list of requirements the spinfoam vertex amplitude has to satisfy in order to provide the causal evolution of spin-network states [ref] .
The Construction of Spin Foam Vertex Amplitudes · Spin foam vertex as a Feynman interaction vertex for GFT · 0.94
-
The role of causality in the spinfoam framework has been studied since the early literature [ref] .
Causal Structure for Generalized Spinfoams · Introduction · 0.99
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.