Fock - Bargmann representation of the distorted Heisenberg algebra

1996 ◽  
Vol 29 (12) ◽  
pp. 3281-3288 ◽  
Author(s):  
J Oscar Rosas-Ortiz
Keyword(s):  
Heisenberg Algebra ◽  
Bargmann Representation

scholarly journals A polynomial class of u(2) algebras

2015 ◽  
Vol 12 (08) ◽  
pp. 1560025
Author(s):  
Mohammed Daoud ◽  
Won Sang Chung
Keyword(s):  
Hilbert Space ◽  
Polynomial Algebra ◽  
Heisenberg Algebra ◽  
Parameter Family ◽  
Unitary Representations ◽  
Contraction Procedure ◽  
Bargmann Representation ◽  
Polynomial Class

A r-parameter u{κ1,κ2,…,κr}(2) algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl–Heisenberg algebra 𝒜{κ1,κ2,…,κr} [M. Daoud and M. Kibler, J. Phys. A: Math. Theor.45 (2012) 244036]. A pair of nonlinear (quadratic) bosons of type 𝒜κ ≡ 𝒜{κ1=κ,κ2=0,…,κr=0} is used to construct, à la Schwinger, a one parameter family of (cubic) uκ(2) algebra. The corresponding Hilbert space is constructed. The analytical Bargmann representation is also presented.

SQUEEZED STATES AND TWO-PARAMETER QUANTUM GROUPS

1998 ◽  
Vol 13 (11) ◽  
pp. 887-891
Author(s):  
VIVEK SAHAI ◽  
RAMANDEEP S. JOHAL ◽  
RAJ K. GUPTA
Keyword(s):  
Quantum Groups ◽  
Analytic Functions ◽  
Heisenberg Algebra ◽  
Single Parameter ◽  
Parameter Study ◽  
Squeezed States ◽  
Squeezing Operator ◽  
Bargmann Representation ◽  
Two Parameter

We investigate two-parameter deformed Weyl–Heisenberg algebra in the Fock–Bargmann representation. The commutator [aqp,āqp] acts like squeezing operator on the space of the entire analytic functions. We find that the second parameter gets absorbed into the first parameter, yielding the same result for squeezing as in the case of single parameter study.

QUANTUM GROUPS, SQUEEZING, BLOCH, AND THETA FUNCTIONS

1993 ◽  
Vol 07 (20) ◽  
pp. 1321-1329 ◽  
Author(s):  
E. CELEGHINI ◽  
S. DE MARTINO ◽  
S. DE SIENA ◽  
G. VITIELLO ◽  
M. RASETTI
Keyword(s):  
Finite Difference ◽  
Quantum Groups ◽  
Theta Functions ◽  
Heisenberg Algebra ◽  
Quantum Systems ◽  
Difference Operators ◽  
Algebra Structure ◽  
Lattice Quantum ◽  
Bargmann Representation

We realize the deformation of the Weyl–Heisenberg algebra in terms of finite difference operators within the Fock–Bargmann representation. This allows us to incorporate in a unified q-algebra structure, the notions of squeezing and lattice quantum systems resorting to the properties of theta functions.

Bialgebra structures on the Heisenberg algebra

1989 ◽  
Vol 75 (1) ◽  
pp. 315-321
Author(s):  
Michel Cahen ◽  
Christian Ohn
Keyword(s):  
Heisenberg Algebra

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

Quantization of the classical Lie algorithm in the Bargmann representation

1991 ◽  
Vol 209 (2) ◽  
pp. 364-392 ◽  
Author(s):  
Mirko Degli Esposti ◽  
Sandro Graffi ◽  
Jan Herczynski
Keyword(s):  
Bargmann Representation

scholarly journals Gauging the Heisenberg algebra of special quaternionic manifolds

2005 ◽  
Vol 610 (1-2) ◽  
pp. 147-151 ◽  
Author(s):  
R. D'Auria ◽  
S. Ferrara ◽  
M. Trigiante ◽  
S. Vaulà
Keyword(s):  
Heisenberg Algebra ◽  
Quaternionic Manifolds

scholarly journals The Bargmann representation for the quantum mechanics on a sphere

2001 ◽  
Vol 42 (9) ◽  
pp. 4138-4147 ◽  
Author(s):  
K. Kowalski ◽  
J. Rembieliński
Keyword(s):  
Quantum Mechanics ◽  
Bargmann Representation

The Aharonov–Bohm effect and its stationary scattering states from the flat circular annulus U(1) holonomy

2014 ◽  
Vol 11 (10) ◽  
pp. 1450084
Author(s):  
Gabriel Y. H. Avossevou ◽  
Bernadin D. Ahounou
Keyword(s):  
Scattering Problem ◽  
Heisenberg Algebra ◽  
Scattering Data ◽  
Gauge Potential ◽  
Circular Annulus ◽  
Topological Quantum ◽  
Vector Gauge ◽  
Simply Connected ◽  
Aharonov Bohm ◽  
Stationary Scattering

In this paper we study the stationary scattering problem of the Aharonov–Bohm (AB) effect. To achieve this goal we construct a Hamiltonian from the most general representations of the Heisenberg algebra. Such representations are defined on a non-simply-connected manifold which we set as the flat circular annulus. By means of the von Neumann's self-adjoint extensions formalism, the scattering data are then provided. No solenoid is considered in this paper. The corresponding Hamiltonian is based on a topological quantum degree of freedom inherent in such representations. This variable stands for the magnetic vector gauge potential at quantum level. Our outcomes confirm the topological nature of this effect.

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