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) =Σs i g (f i ,X,Ω), where the limit is taken as N→∞, the sum runs from i=1 to r=rank g, Λ=Σμ i f i ,f i are the highest weights of the r fundamental representations of g,s i =lim μ i /N, and g (f i ,X,Ω) is the expectation value of X with respect to the coherent states ‖f i , Ω〉 in the representation Γf i . Examples and applications are given.