Finite Hamiltonian systems: Linear transformations and aberrations

Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su (2), and their phase space is a sphere. Rigid motions of this phase space form the group SU (2); overall phases com...

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Bibliographic Details
Published inPhysics of atomic nuclei Vol. 73; no. 3; pp. 546 - 554
Main Author Wolf, K. B.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.03.2010
Springer
Subjects
Algebra
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EIGENVALUES
Elementary Particles and Fields
HAMILTONIANS
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
OPTICAL SYSTEMS
Particle and Nuclear Physics
PHASE SPACE
Physics
Physics and Astronomy
QUANTIZATION
QUANTUM OPERATORS
SPACE
SPHERES
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TRANSFORMATIONS
U GROUPS
U-2 GROUPS
Phase Space
Poisson Operator
Atomic Nucleus
Wigner Function
Classical Phase Space
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Summary:Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su (2), and their phase space is a sphere. Rigid motions of this phase space form the group SU (2); overall phases complete this to U (2). But since N -point states can be subject to U ( N ) ⊃ U (2) transformations, the rest of the generators will provide all N 2 unitary transformations of the states, which appear as nonlinear transformations—aberrations—of the system phase space. They are built through the “finite quantization” of a classical optical system.
ISSN:1063-7788
1562-692X
DOI:10.1134/S1063778810030191