scholarly journals SUPERCONFORMAL QUANTUM MECHANICS VIA WIGNER–HEISENBERG ALGEBRA

2010 ◽  
Vol 25 (29) ◽  
pp. 2507-2521 ◽  
Author(s):  
H. L. CARRION ◽  
R. DE LIMA RODRIGUES
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Casimir Operator ◽  
Conformal Symmetry ◽  
Heisenberg Algebra ◽  
Raising And Lowering Operators ◽  
Parity Operator ◽  
Conformal Quantum Mechanics ◽  
Lowering Operators ◽  
Natural Relation

We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. A model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner–Heisenberg algebra picture [x, px] = i(1+cP) (P being the parity operator) is presented. In this context, the energy spectrum, the Casimir operator, raising and lowering operators are defined.

scholarly journals DEFORMED CONFORMAL AND SUPERSYMMETRIC QUANTUM MECHANICS

1992 ◽  
Vol 07 (14) ◽  
pp. 1241-1251 ◽  
Author(s):  
VYACHESLAV SPIRIDONOV
Keyword(s):  
Quantum Mechanics ◽  
Conformal Symmetry ◽  
Symmetry Algebra ◽  
The Self ◽  
Supersymmetry Algebra ◽  
Standard Quantum ◽  
Physical Systems ◽  
Raising And Lowering Operators ◽  
Self Similar ◽  
Lowering Operators

Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e., the spectrum of one can be obtained from another (with possible exception of the lowest level) by the q2-factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra su q(1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.

scholarly journals Factorization Method in Oscillator with the Aharonov-Casher System

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
J. Sadeghi ◽  
Jalil Naji ◽  
Behnam Pourhassan
Keyword(s):  
Wave Function ◽  
Energy Spectrum ◽  
Factorization Method ◽  
Mathematical Foundation ◽  
Raising And Lowering Operators ◽  
General Wave ◽  
Lowering Operators

We review the oscillator with Aharonov-Casher system and study some mathematical foundation about factorization method. The factorization method helps us to obtain the energy spectrum and general wave function for the corresponding system in some spin condition. The factorization method leads us to obtain the raising and lowering operators for the Aharonov-Casher system. The corresponding operators give us the generators of the algebra.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

New structure in the energy spectrum of reggeon quantum mechanics with quartic couplings

1980 ◽  
Vol 91 (2) ◽  
pp. 291-295 ◽  
Author(s):  
Benjamin C. Harms ◽  
Stanley T. Jones ◽  
Chung-I Tan
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum

scholarly journals Conformal quantum mechanics as the CFT1 dual to AdS2

2011 ◽  
Vol 701 (4) ◽  
pp. 503-507 ◽  
Author(s):  
Claudio Chamon ◽  
Roman Jackiw ◽  
So-Young Pi ◽  
Luiz Santos
Keyword(s):  
Quantum Mechanics ◽  
Conformal Quantum Mechanics

scholarly journals A demonstration that electroweak theory can violate parity automatically (leptonic case)

2018 ◽  
Vol 33 (04) ◽  
pp. 1830005 ◽  
Author(s):  
C. Furey
Keyword(s):  
Clifford Algebra ◽  
Ad Hoc ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Ladder Operators ◽  
Raising And Lowering Operators ◽  
Ladder Operator ◽  
Left And Right ◽  
Electroweak Model ◽  
Lowering Operators

We bring to light an electroweak model which has been reappearing in the literature under various guises.[Formula: see text] In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra [Formula: see text]. That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by [Formula: see text] and [Formula: see text]. Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.

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