Coherent states of the \(q\)-canonical commutation relations

DOI10.1007/BF02101486zbMath0838.46056arXivfunct-an/9303002OpenAlexW1842297855WikidataQ62124863 ScholiaQ62124863MaRDI QIDQ1908823

Reinhard F. Werner, Palle E. T. Jorgensen

Publication date: 7 March 1996

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

Full work available at URL: https://arxiv.org/abs/funct-an/9303002

zbMATH Keywords

canonical commutation relationsFock representationCuntz algebracoherent statesuniversal \(C^*\)-algebra

Mathematics Subject Classification ID

Applications of selfadjoint operator algebras to physics (46L60) Commutation relations and statistics as related to quantum mechanics (general) (81S05) States of selfadjoint operator algebras (46L30) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (17)

On commutators of Wick products on CCR and CAR algebras ⋮ Symmetry in tensor algebras over Hilbert space ⋮ Noncommutative Kähler-like structures in quantization ⋮ On fractional Brownian motion and wavelets ⋮ CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras ⋮ Multiresolution wavelet analysis of integer scale Bessel functions ⋮ Hopf-type deformed oscillators, their quantum double and a \(q\)-deformed Calogero-Vasiliev algebra. ⋮ Generalized cyclic cohomology associated with deformed commutators ⋮ Generating \(q\)-commutator identities and the \(q\)-BCH formula ⋮ STATES ON THE CUNTZ ALGEBRAS AND p-ADIC RANDOM WALKS ⋮ Two-sided ideals in \(q\)-deformed Heisenberg algebras. ⋮ Markov measures and extended zeta functions ⋮ REPRESENTATIONS OF LIE ALGEBRAS BUILT OVER HILBERT SPACE ⋮ Bilinear forms, Clifford algebras, \(q\)-commutation relations, and quantum groups ⋮ The \(q\)-deformed Campbell-Baker-Hausdorff-Dynkin theorem ⋮ Wavelet representations and Fock space on positive matrices ⋮ On \(*\)-representations of a deformation of a Wick analogue of the CAR algebra

Cites Work

• Unnamed Item
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• An example of a generalized Brownian motion
• A dichotomy for derivations on \({\mathcal O}_ n\)
• A new example of `independence' and `white noise'
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Stochastic integration on the Cuntz algebra \({\mathcal O}_ \infty\)
• \(R\)-commutative geometry and quantization of Poisson algebras
• Realizability of a model in infinite statistics
• Simple \(C^*\)-algebras generated by isometries
• The general form of non-Fock coherent boson states
• Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule
• Positive representations of general commutation relations allowing Wick ordering
• States of the Clifford algebra
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The quantum group SU_q(2) and a q-analogue of the boson operators
• A q-analogue of the Campbell-Baker-Hausdorff expansion
• A deformation of quantum mechanics
• Interpolation between Fermi and Bose statistics using generalized commutators
• On the Fock representation of the q-commutation relations
• A Commutativity Theorem for Normal Operators

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