The q-analog of the boson algebra, its representation on the Fock space, and applications to the quantum group

DOI10.1063/1.529400zbMath0736.17012OpenAlexW2060636273MaRDI QIDQ3981616

Mo-Lin Ge, Chang-pu Sun

Publication date: 26 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529400

zbMATH Keywords

quantum grouprepresentations\(q\)-analog of the Heisenberg-Weyl algebra\(q\)-deformed boson operators\(q\)-deformed differential realization

Mathematics Subject Classification ID

Related Items (7)

A new q-deformed boson realization of quantum algebra slq(n+1) and nongeneric slq(2) R-matrices ⋮ Finite dimensional irreducible representations of the quantum algebra Uq(C2) ⋮ THE CNOT QUANTUM LOGIC GATE USING q-DEFORMED OSCILLATORS ⋮ Irreducible highest weight representations of quantum groups \(U_ q(gl(n,\mathbb{C}{}))\) ⋮ Representations of Uεres(sl2) via restricted q-Fock spaces ⋮ QUANTUM LOGIC GATES USING q-DEFORMED OSCILLATORS ⋮ Coherent states in the form of a quantum group

Cites Work

• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• The quantum group SU_q(2) and a q-analogue of the boson operators
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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