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Classical Systems and Representations of (2+1) Newton-Hooke Symmetries

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Oscar Arratia, Miguel A. Martin, Mariano A. Olmo

Mathematical Physics · Submitted 8 Mar 1999

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The authors' main claim A complete classification is given by explicit computation.

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arXiv IDmath-ph/9903013 (version 1)
Pith IDWLYJAN5G, Pith's permanent record of this paper and its review
CitationMariano A. Olmo, Miguel A. Martin, Oscar Arratia. "Classical Systems and Representations of (2+1) Newton-Hooke Symmetries." arXiv:math-ph/9903013 (1999). https://pith.science/paper/WLYJAN5G
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,797 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.02.

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

This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal scheme.

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 This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. contribution 0.93 0.85 0.08 asserted 0.97
s1 A complete classification is given by explicit computation. result 0.56 0.93 0.40 asserted 1.00
s2 In addition, we present an application example of quantization using the Moyal scheme. contribution 0.92 0.92 0.09 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.94.

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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

This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal scheme.

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References
How the literature uses it

8 arXiv papers cite this in 12 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 · 8 sentences without a confident label

Uses its method or tool 1 paper
Cites it as background 3 papers
  • In comparison with the Galilei algebra, described by the generators $J_ij$ (nonrelativistic rotation), $P_i$ (space translations), $K_i$ (nonrelativistic boots) and $H$ (time translations) in NH algebra one relation is deformed for the finite value $R$ of nonrelativistic $(A)dS$ radius [equation] In arbitrary dimension $D$ one can introduce one central charge described by the mass parameter $m$ [equation] If $D=2+1$ one can add second “exotic" central charge $θ$ [ref] [equation] Recently the NH symmetries were enlarged by adding the constant accelerations, described by the generator $F_i$ [ref] .

    Enlarged NH symmetries: Particle Dynamics and Gauge Symmetries · Introduction · 0.94

  • Examples of doubly centrally extended symmetries are provided by exotic Galilei [ref] , and exotic Newton-Hooke (ENH) [ref] symmetries.

    Super-extended noncommutative Landau problem and conformal symmetry · Introduction · 0.81

  • There is considerable literature on Newton-Hooke symmetries and spacetimes both in 3+1 and 2+1 dimensions, starting with the classic paper [ref] and continuing with recent studies of the (2+1)-dimensional [ref] and (3+1)-dimensional [ref] situation.

    Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra · Lie algebra and group structure · 1.00

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