Symmetric Lie algebras of non-linear transformations of conformal type in quantum mechanics

Journal Article · Mon Jan 01 04:00:00 EST 1973 · Int. J. Theor. Phys., v. 7, no. 5, pp. 379-388

DOI:https://doi.org/10.1007/BF00669916· OSTI ID:4388996

Tilgner, H

The Koecher construction of simple symmetric Lie algebras is used to realize colineation and conformal Lle algebras of nonlinear transformations of a pseudo-orthogonal vector space in the canonical Weyl algebras, which are used in the Schroedinger representation. The realization maps the linear sub-algebras onto symmetrized polynomials of second degree, whereas the nonlinear parts are mapped onto polynomials of flrst and third degree. For the two examples the Meyberg Jordan algebras are explicitly given. (auth)

• Research Organization: Univ., Marburg, Ger.
• NSA Number: NSA-29-001490
• OSTI ID: 4388996
• Journal Information: Int. J. Theor. Phys., v. 7, no. 5, pp. 379-388, Journal Name: Int. J. Theor. Phys., v. 7, no. 5, pp. 379-388; ISSN IJTPB
• Country of Publication: United Kingdom
• Language: English

Related Subjects

*LIE GROUPS-- ALGEBRA
*SCHROEDINGER EQUATION-- LIE GROUPS
CANONICAL TRANSFORMATIONS
N64310* --Physics (High Energy)--Particle Invariance Principles & Symmetry--General
NONLINEAR PROBLEMS
POLYNOMIALS
QUANTUM MECHANICS
SYMMETRY
VECTORS