scholarly journals Joint torsion of several commuting operators

2012 ◽  
Vol 229 (1) ◽  
pp. 442-486 ◽  
Author(s):  
J. Kaad
Keyword(s):  
Commuting Operators ◽  
Joint Torsion

scholarly journals Tate tame symbol and the joint torsion of commuting operators

2020 ◽  
Vol 5 (2) ◽  
pp. 181-211
Author(s):  
Jens Kaad ◽  
Ryszard Nest
Keyword(s):  
Commuting Operators ◽  
Joint Torsion

Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)

1974 ◽  
Vol 15 (10) ◽  
pp. 1787-1799 ◽  
Author(s):  
B. R. Judd ◽  
W. Miller ◽  
J. Patera ◽  
P. Winternitz
Keyword(s):  
Enveloping Algebra ◽  
Commuting Operators ◽  
Complete Sets

scholarly journals Quantized toroidal dipole eigenvalues in nano-systems

2021 ◽  
Vol 2090 (1) ◽  
pp. 012151
Author(s):  
D. V. Anghel ◽  
A. T. Preda
Keyword(s):  
Parity Violation ◽  
Nuclear Reactions ◽  
General Procedure ◽  
Quantum Systems ◽  
Electromagnetic Structure ◽  
New Class ◽  
Quantum Properties ◽  
Commuting Operators ◽  
Dipole Operator ◽  
Theoretical Considerations

Abstract The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. This corresponds to the toroidal dipole operator T ^ in quantum systems, with the projections T ^ i (i = 1, 2, 3) on the coordinate axes. These operators are observables if they are self-adjoint, but, although it is commonly discussed of toroidal dipoles of both, classical and quantum systems, up to now no system has been identified in which the operators are self-adjoint. Therefore, in this paper we use what are called the “natural coordinates” of the T ^ 3 operator to give a general procedure to construct operators that commute with T ^ 3 . Using this method, we introduce the operators p ^ ( k ) , p ^ ( k 1 ) , and p ^ ( k 2 ) , which, together with T ^ 3 and L ^ 3 , form sets of commuting operators: ( p ^ ( k ) , T ^ 3 , L ^ 3 ) and ( p ^ ( k 1 ) , p ^ ( k 2 ) , T ^ 3 ) . All these theoretical considerations open up the possibility to design metamaterials that could exploit the quantization and the general quantum properties of the toroidal dipoles.

POISSON STRUCTURE AND INTEGRABILITY OF THE NEUMANN-MOSER-UHLENBECK MODEL

1990 ◽  
Vol 05 (23) ◽  
pp. 4477-4488 ◽  
Author(s):  
J. AVAN ◽  
M. TALON
Keyword(s):  
Poisson Structure ◽  
Point Of View ◽  
Conserved Quantities ◽  
Poisson Brackets ◽  
Quantum Level ◽  
Quantum Integrability ◽  
Commuting Operators ◽  
Lax Operator

Neumann’s model, describing the motion of a particle on an N-sphere under harmonic forces, is studied from the point of view of classical and quantum integrability. Classical integrability is derived from a generalized structure, “R-S couple” or “D-matrix” for the Poisson brackets of the Lax operator. The already-known set of conserved quantities for this model turns out to follow straightforwardly from this structure. It gives rise to a set of commuting operators at the quantum level, and the algebra of Lax operators directly follows from the classical one.

Representations by Commuting Operators

1995 ◽  
pp. 409-521
Author(s):  
Y. M. Berezansky ◽  
Y. G. Kondratiev
Keyword(s):  
Commuting Operators
Sign in / Sign up

Export Citation Format

Share Document