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Quantum Space-time and Classical Gravity
General Relativity and Quantum Cosmology · Submitted 24 Jul 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Perturbations of this calculus are shown to give rise to non-trivial gravitational fields.
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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.
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The abstract, sentence by sentence
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a natural differential calculus using which the space-time is necessarily flat Minkowski space-time. Perturbations of this calculus are shown to give rise to non-trivial gravitational fields.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. | background 0.96 | 0.07 | 0.04 | asserted 0.99 |
| s1 | As an example a version of quantized space-time is considered here. | contribution 0.61 | 0.54 | 0.03 | asserted 0.80 |
| s2 | It is found that there is a natural differential calculus using which the space-time is necessarily flat Minkowski space-time. | result 1.00 | 0.88 | 0.46 | asserted 1.00 |
| s3 | Perturbations of this calculus are shown to give rise to non-trivial gravitational fields. | result 0.99 | 0.87 | 0.51 | asserted 1.00 |
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The paper
Original abstract
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a natural differential calculus using which the space-time is necessarily flat Minkowski space-time. Perturbations of this calculus are shown to give rise to non-trivial gravitational fields.
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References
How the literature uses it
5 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 1 paper
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If we apply the Cartan frame formalism [ref] to this quadratic algebra, we obtain a noncommutative differential calculus, whose one-forms are generated by the frame ${θ^i}$, where $θ^i:(_1^(n))→$ satisfies $θ^i(_p_j)=δ^i_j$.
On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory · Noncommutative scalar curvature · 0.99
Compares with it 1 paper
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It is also reminiscent to ideas in [ref] , in the sense that gravity is determined by noncommutativity i.e. the Poisson structure.
Emergent Gravity from Noncommutative Gauge Theory · Discussion · 0.84
Cites it as background 2 papers
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While several formulations of NC gravity have been proposed by deforming various formulations of general relativity [ref] , a simple and compelling mechanism would be very desirable.
Emergent Gravity from Noncommutative Gauge Theory · Introduction · 0.98
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See also [ref] for a collection of approaches towards NC gravity.
Field Theory on Curved Noncommutative Spacetimes · Introduction · 0.99
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