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Two-photon algebra deformations

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Preeti Parashar, Angel Ballesteros, Francisco J. Herranz

Quantum Algebra · Submitted 26 Jul 1999

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

The authors' main claim Two non-standard quantum deformations of $h_6$, together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra.

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arXiv IDmath/9907170 (version 1)
Pith IDMUGQSFAX, Pith's permanent record of this paper and its review
CitationAngel Ballesteros, Francisco J. Herranz, Preeti Parashar. "Two-photon algebra deformations." arXiv:math/9907170 (1999). https://pith.science/paper/MUGQSFAX
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arXiv listing abstract v1. Results and the main claim are underlined; .

In order to obtain a classification of all possible quantum deformations of the two-photon algebra $h_6$, we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of $h_6$, together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra. One-boson representations for these quantum two-photon algebras are derived and translated into Fock--Bargmann realizations. In this way, a systematic study of `deformed' states of light in quantum optics can be developed.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In order to obtain a classification of all possible quantum deformations of the two-photon algebra $h_6$, we introduce its corresponding general Lie bialgebra, which is a coboundary one. method 0.56 0.91 0.12 asserted 0.99
s1 Two non-standard quantum deformations of $h_6$, together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra. result 0.82 0.93 0.40 asserted 1.00
s2 One-boson representations for these quantum two-photon algebras are derived and translated into Fock--Bargmann realizations. result 0.47 0.93 0.10 asserted 1.00
s3 In this way, a systematic study of `deformed' states of light in quantum optics can be developed. interpretation 0.79 0.20 0.24 hedged possibility 0.81

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Original abstract

In order to obtain a classification of all possible quantum deformations of the two-photon algebra $h_6$, we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of $h_6$, together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra. One-boson representations for these quantum two-photon algebras are derived and translated into Fock--Bargmann realizations. In this way, a systematic study of `deformed' states of light in quantum optics can be developed.

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