The classical limit of quantum nonspin systems

Abstract

The classical limit of operators X belonging to any compact Lie algebra g is computed. If X∈g, the classical limit in the representation ΓΛ, whose highest weight is Λ, is lim ΓΛ(X/N) =Σsig (fi,X,Ω), where the limit is taken as N→∞, the sum runs from i=1 to r=rank g, Λ=Σμifi,fi are the highest weights of the r fundamental representations of g,si=lim μi/N, and g (fi,X,Ω) is the expectation value of X with respect to the coherent states ‖fi, Ω〉 in the representation Γfi. Examples and applications are given.