GENERALIZED QUANTUM SPINS, COHERENT STATES, AND LIEB INEQUALITIES

A mathematical generalization of the concept of quantum spin is constructed in which the role of the symmetry group O3 is replaced by Ov (ν=2,3,4, ...). The notion of spin direction is replaced by a point on the manifold of oriented planes in ℝv. The theory of coherent states is developed, and it is shown that the natural generalizations of Lieb's formulae connecting quantum spins and classical configuration space hold true. This leads to the Lieb inequalities [1] and with it to the limit theorems as the quantum spin l approaches infinity. The critical step in the proofs is the validity of the appropriate generalization of the Wigner-Eckart theorem. © 1979 Springer-Verlag.