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Vector Coherent States from Plancherel's Theorem, Clifford Algebras and Matrix Domains

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S. Twareque Ali, Miroslav Englis, Jean-Pierre Gazeau

Mathematical Physics · Submitted 24 Nov 2003

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

The authors' main claim As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit.

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arXiv IDmath-ph/0311042 (version 1)
Pith IDULDVKZC4, Pith's permanent record of this paper and its review
CitationJean-Pierre Gazeau, Miroslav Englis, S. Twareque Ali. "Vector Coherent States from Plancherel's Theorem, Clifford Algebras and Matrix Domains." arXiv:math-ph/0311042 (2003). https://pith.science/paper/ULDVKZC4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,613 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit. These vector coherent states may have a finite or an infinite number of components. As examples we first apply the technique to construct vector coherent states using the Plancherel isometry for groups and vector coherent states associated to Clifford algebras, in particular quaternions. As physical examples, we discuss vector coherent states for a quantum optical model and finally apply the general technique to build vector coherent states over certain matrix domains.

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 As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit. contribution 0.99 0.90 0.49 asserted 1.00
s1 These vector coherent states may have a finite or an infinite number of components. contribution 0.57 0.46 0.05 hedged possibility 0.99
s2 As examples we first apply the technique to construct vector coherent states using the Plancherel isometry for groups and vector coherent states associated to Clifford algebras, in particular quaternions. contribution 0.56 0.89 0.09 asserted 0.99
s3 As physical examples, we discuss vector coherent states for a quantum optical model and finally apply the general technique to build vector coherent states over certain matrix domains. contribution 0.92 0.92 0.15 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 1.00.

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  • S sections
  • T body sentences
  • C citations
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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

As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit. These vector coherent states may have a finite or an infinite number of components. As examples we first apply the technique to construct vector coherent states using the Plancherel isometry for groups and vector coherent states associated to Clifford algebras, in particular quaternions. As physical examples, we discuss vector coherent states for a quantum optical model and finally apply the general technique to build vector coherent states over certain matrix domains.

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