Realizations of the central extension of the inhomogeneous symplectic algebra as time dependent invariance algebras of nonrelativistic quantum systems

Journal Article · Fri Aug 01 00:00:00 EDT 1975 · J. Math. Phys. (N.Y.), v. 16, no. 8, pp. 1692-1703

DOI:https://doi.org/10.1063/1.522738· OSTI ID:4141439

Burdet, G; Perrin, M

The one-element central extension of the Lie algebra of the group of real inhomogeneous linear canonical transformations of phase space is interpreted as a time-dependent invariance algebra in the Schroedinger picture. By limiting to a two-dimensional space quantum system one can exhibit all the nonconjugate Hamiltonians contained in the symplectic algebra which, in the Heisenberg picture, plays the role of dynamical algebra and contains several known degeneracy and spectrum-generating algebras. (3 figures, 2 tables) (auth)

• Research Organization: Centre National de la Recherche Scientifique, Marseille
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-008615
• OSTI ID: 4141439
• Journal Information: J. Math. Phys. (N.Y.), v. 16, no. 8, pp. 1692-1703, Other Information: Orig. Receipt Date: 30-JUN-76
• Country of Publication: United States
• Language: English

Related Subjects

N76100* -Physics (Theoretical)-General
N64310 -Physics (High Energy)-Particle Invariance Principles & Symmetry-General
644002*
*LIE GROUPS- ALGEBRA
*SCHROEDINGER PICTURE- QUANTUM OPERATORS
CANONICAL TRANSFORMATIONS
HAMILTONIANS
HARMONIC OSCILLATORS
SP GROUPS
TIME DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS