scholarly journals FOUR KINDS OF RAISING AND LOWERING OPERATORS-OF TWO-AND THREE-DIMENSIONAL HYDROGEN ATOMS

1997 ◽  
Vol 46 (3) ◽  
pp. 428
Author(s):  
LIU YU-FENG ◽  
ZENG JIN-YAN
Keyword(s):  
Three Dimensional ◽  
Hydrogen Atoms ◽  
Raising And Lowering Operators ◽  
Lowering Operators

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)).

Ab Initio Determination of a New Complex Structure (55 Non-Hydrogen Atoms) from Synchrotron Powder Data: An Uncommon Nickel Succinate, Ni7(C4H4O4)4(OH)6(H2O)3•7H2O

2004 ◽  
Vol 443-444 ◽  
pp. 333-336
Author(s):  
N. Guillou ◽  
C. Livage ◽  
W. van Beek ◽  
G. Férey
Keyword(s):  
Ab Initio ◽  
Complex Structure ◽  
Three Dimensional ◽  
Free Water ◽  
Hydrogen Atoms ◽  
Monoclinic System ◽  
Synchrotron Powder Diffraction ◽  
Chloride Hexahydrate ◽  
Autogenous Pressure

Ni7(C4H4O4)4(OH)6(H2O)3. 7H2O, a new layered nickel(II) succinate, was prepared hydrothermally (180°C, 48 h, autogenous pressure) from a 1:1.5:4.1:120 mixture of nickel (II) chloride hexahydrate, succinic acid, potassium hydroxide and water. It crystallizes in the monoclinic system (space group P21/c, Z = 4) with the following parameters a = 7.8597(1) Å, b = 18.8154(3)Å, c = 23.4377(4) Å,ϐ = 92.0288(9)°, and V = 3463.9(2) Å3. Its structure, which contains 55 non-hydrogen atoms, was solved ab initio from synchrotron powder diffraction data. It can be described from hybrid organic-inorganic layers, constructed from nickel oxide corrugated chains. These chains are built up from NiO6hexameric units connected via a seventh octahedron. Half of the succinates decorate the chains, and the others connect them to form the layers. The three dimensional arrangement is ensured by hydrogen bonds directly between two adjacent layers and via free water molecules.

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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