scholarly journals Proof by characters of the orthogonal-orthogonal duality and relations of Casimir invariants

2019 ◽  
Vol 60 (8) ◽  
pp. 081705 ◽  
Author(s):  
K. Neergård
Keyword(s):  
Casimir Invariants

General indices of representations and Casimir invariants

1984 ◽  
Vol 25 (2) ◽  
pp. 219-227 ◽  
Author(s):  
S. Okubo ◽  
J. Patera
Keyword(s):  
Casimir Invariants

Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions

2015 ◽  
Vol 774 ◽  
pp. 443-459 ◽  
Author(s):  
Y. Chikasue ◽  
M. Furukawa
Keyword(s):  
Simulated Annealing ◽  
Finite Number ◽  
Stationary State ◽  
Two Dimensions ◽  
Annealing Process ◽  
Initial Condition ◽  
Vorticity Field ◽  
Casimir Invariants

A method is developed to adjust a vorticity field to satisfy specified values for a finite number of Casimir invariants. The developed method is tested numerically for a neutral fluid in two dimensions. The adjusted vorticity field is adopted as an initial condition for simulated annealing (SA) of an incompressible, ideal neutral fluid and its magnetohydrodynamics (MHD), where SA enables us to obtain a stationary state of the fluid. Since the Casimir invariants are kept unchanged during the annealing process, the obtained stationary state has the required values of the Casimir invariants specified by our method.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

scholarly journals Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants

1988 ◽  
Vol 304 ◽  
pp. 348-370 ◽  
Author(s):  
F.A. Bais ◽  
P. Bouwknegt ◽  
M. Surridge ◽  
K. Schoutens
Keyword(s):  
Virasoro Algebra ◽  
Higher Order ◽  
Casimir Invariants

scholarly journals Computing Casimir invariants from Pffafian systems

1999 ◽  
Vol 260 (6) ◽  
pp. 475-483 ◽  
Author(s):  
T.W. Yudichak ◽  
Benito Hernández-Bermejo ◽  
P.J. Morrison
Keyword(s):  
Casimir Invariants

scholarly journals Casimir invariants and characteristic identities for gl(∞)

1997 ◽  
Vol 38 (9) ◽  
pp. 4783-4793 ◽  
Author(s):  
M. D. Gould ◽  
N. I. Stoilova
Keyword(s):  
Casimir Invariants
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