Affine Models of Internal Degrees of Freedom and their Quantization

Abstract

We discuss some classical and quantization problems of infinitesimal affinely-rigid bodies moving in two-dimensional manifolds. Considered are highly symmetric models for which the variables can be separated. We follow the standard procedure of quantization in Riemannian manifolds, i.e., we use the ${\rm L}^{2}$-Hilbert space of wave functions in the sense of the usual Riemannian measure (volume element).