Trace formulas for the Casimir operators of the unextended Schrödinger algebra S(N)

Abstract

Using the contraction of the centrally extended Schrödinger algebra Ŝ(N) onto the Lie algebra S(N) ⊕ R in combination with the Newton identities associated with the characteristic polynomial of a matrix, we derive explicit expressions for the Casimir operators of the unextended Schrödinger algebra S(N) in terms of trace operators. It is shown that these operators can be defined independently of the contraction from which a direct method for the computation of the S(N)-invariants is deduced.