SL (6,R) AS THE GROUP OF SYMMETRIES FOR NON RELATIVISTIC QUANTUM SYSTEMS

Abstract

It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of the group action on Ĥ, we have a generalized rotation of state vectors in which the norms are preserved. Thus one obtains new symmetries as well as new representations which aid in the simplification of the system. New solutions can thus be obtained, which in most cases have realistic physical properties.


KEY WORDS: Prolongations, Symmetry Groups, Sets of States.


Global Jnl of Mathematical Sciences Vol. 31) 2004: 35-46