Boson and differential realizations of polynomial angular momentum algebra

2001 ◽  
Vol 42 (6) ◽  
pp. 2718-2724 ◽  
Author(s):  
Dong Ruan ◽  
Yufeng Jia ◽  
Wei Ruan
Keyword(s):  
Angular Momentum ◽  
Angular Momentum Algebra

The angular pattern in the hyperfine structure of Xe I and Kr I atoms

2021 ◽  
Author(s):  
Christophe Blondel ◽  
Cyril Drag
Keyword(s):  
Angular Momentum ◽  
Hyperfine Structure ◽  
Noble Gases ◽  
Outer Electron ◽  
Angular Momenta ◽  
Atomic States ◽  
Angular Momentum Algebra ◽  
Simple Picture ◽  
The Way

Abstract Recent reviews of the hyperfine structure of xenon and krypton have highlighted the variety of the values taken by the hyperfine coefficients A and B of these atoms. These variations, as functions of the atomic angular momenta, were however not explained quantitatively. This article shows the simple picture and angular momentum algebra that make it possible to account for the observed trend. The only necessary approximations are to consider the interaction of the outer electron negligible with respect to the coupling of the p5 core with the nucleus, and to assume that the Racah ||(p5)j l[K]J F〉basis, conventionally used for the atomic states of noble gases, makes a fitting description of the hierarchy of their angular momentum couplings. The way the calculation corroborates the apparently erratic values of hyperfine coefficients A and B in Xe I and Kr I shows up as a confirmation of the validity of these approximations.

SINGLE BOSON AND INVERSION BOSON REALIZATIONS OF MULTI-PARAMETER NONLINEARLY DEFORMED ANGULAR MOMENTUM ALGEBRA

2013 ◽  
Vol 28 (28) ◽  
pp. 1350113
Author(s):  
DONG RUAN ◽  
HUA-JUN HUANG ◽  
YOU-NING LI
Keyword(s):  
Angular Momentum ◽  
Polynomial Function ◽  
Fock Space ◽  
And Inversion ◽  
Angular Momentum Algebra

Explicit, analytic and closed expressions for boson realizations of the (m+3)-parameter nonlinearly deformed angular momentum algebra [Formula: see text] with its highest power m of polynomial function being arbitrary, which combines and generalizes Witten's two deformation schemes, are investigated in terms of the single boson and the single inversion boson, respectively. For each kind, the unitary Holstein–Primakoff-like realization, the non-unitary Dyson–Maléev-like realization and their connections are respectively discussed. Using these realizations, the corresponding representations of [Formula: see text] as well as their respective acting spaces in the Fock space are obtained.

GUP and its Application to Angular Momentum Algebra

2020 ◽  
Vol 59 (8) ◽  
pp. 2617-2624
Author(s):  
Seyed Amin Khorram-Hosseini ◽  
Hossein Panahi ◽  
Saber Zarrinkamar
Keyword(s):  
Angular Momentum ◽  
Angular Momentum Algebra

scholarly journals THE ANTICOMMUTATOR SPIN ALGEBRA, ITS REPRESENTATIONS AND QUANTUM GROUP INVARIANCE

2003 ◽  
Vol 18 (27) ◽  
pp. 5039-5045 ◽  
Author(s):  
M. ARIK ◽  
U. KAYSERILIOGLU
Keyword(s):  
Angular Momentum ◽  
Quantum Group ◽  
The Other ◽  
Defining Relations ◽  
Integer Spin ◽  
Half Integer ◽  
Dimension Formula ◽  
Group Invariance ◽  
Spin Representations ◽  
Angular Momentum Algebra

We define a 3-generator algebra obtained by replacing the commutators with anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the angular momentum algebra. The half-integer spin representations, on the other hand, split into two representations of dimension [Formula: see text]. The anticommutator spin algebra is invariant under the action of the quantum group SO q(3) with q=-1.

scholarly journals The total angular momentum algebra related to the S3 Dunkl Dirac equation

2018 ◽  
Vol 389 ◽  
pp. 192-218 ◽  
Author(s):  
Hendrik De Bie ◽  
Roy Oste ◽  
Joris Van der Jeugt
Keyword(s):  
Angular Momentum ◽  
Dirac Equation ◽  
Total Angular Momentum ◽  
Angular Momentum Algebra
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