Effective Casimir Conditions and Group Coherent States

Abstract

Properties of group coherent states can be derived "effectively" without knowing full wave functions. The procedure is detailed in this article as an example of general methods for effective constraints. The role of constraints in the present context is played by a Casimir condition that puts states within an irreducible representation of a Lie group (or, equivalently, on a quantization of a co-adjoint orbit of the dual Lie algebra). Simplifications implied by a Casimir condition, compared with general first-class constraints, allows one to show that the correct number of degrees of freedom is obtained after imposing the condition. When combined with conditions to saturate uncertainty relations, moments of group coherent states can be derived. A detailed example in quantum cosmology (cosmic forgetfulness) illustrates the usefulness of the methods.