An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.

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SU(d)-INVARIANT MULTIDIMENSIONAL q-OSCILLATORS WITH BOSONIC DEGENERACY

Modern Physics Letters A ◽

10.1142/s0217732300001535 ◽

2000 ◽

Vol 15 (19) ◽

pp. 1237-1242 ◽

Cited By ~ 3

Author(s):

A. ALGIN ◽

M. ARIK ◽

N. M. ATAKISHIYEV

Keyword(s):

Harmonic Oscillator ◽

Quantum Group ◽

Lie Group ◽

The Other ◽

Quantum Harmonic Oscillator ◽

Standard Quantum ◽

Newton Equation ◽

Two Parameter

Multidimensional two-parameter (q1, q2)-oscillators are of two kinds: one is invariant under the (ordinary) Lie group SU (d), whereas the other is invariant under the quantum group SU q(d) where q = q1/q2. It is shown that the q1 = q2 limit of both of these two-parameter oscillators coincide and give the q-deformed Newton oscillator which can be derived from the standard quantum harmonic oscillator Newton equation. The bosonic degeneracies of the excited levels of these oscillators are different for q1 ≠ q2, but coincide in the q1 = q2 limit.

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Anomalous Dissipative Quantum Harmonic Oscillator

Communications in Theoretical Physics ◽

10.1088/0253-6102/49/1/31 ◽

2008 ◽

Vol 49 (1) ◽

pp. 137-142 ◽

Cited By ~ 2

Author(s):

Bai Zhan-Wu

Keyword(s):

Harmonic Oscillator ◽

Quantum Harmonic Oscillator

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The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

Journal of High Energy Physics ◽

10.1007/jhep07(2021)221 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Nikolay Bobev ◽

Friðrik Freyr Gautason ◽

Jesse van Muiden

Keyword(s):

String Theory ◽

Three Dimensional ◽

Parameter Family ◽

Global Symmetry ◽

Maximal Supergravity ◽

All Solutions ◽

Operator Spectrum ◽

Type Iib String Theory ◽

Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

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