On reduction of the four-dimensional harmonic oscillator
- 1 August 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (8) , 1628-1632
- https://doi.org/10.1063/1.525104
Abstract
This paper deals with reduction of the four-dimensional harmonic oscillator by use of a one-parameter subgroup U(1) of the symmetry group SU(4), U(1) being the symmetry subgroup generated by an ’’angular momentum.’’ The angular momentum determines in the energy surface S7 an ’’energy-momentum’’ manifold S3×S3 on which a subgroup SU(2)×SU(2) of SU(4) acts. The reduction process yields a manifold S3×S2 = S3×S3/U(1) on which SO(4) acts effectively.Keywords
This publication has 2 references indexed in Scilit:
- Reduction of symplectic manifolds with symmetryPublished by Elsevier ,2002
- A general setting for reduction of dynamical systemsJournal of Mathematical Physics, 1979