Quantized Affine Motion, Internal Excitation and Some Raman-like Phenomena

Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on some invariance properties under the action of isometric and affine transformations we reviewed some new models of the mutual interaction between rotational and deformative degrees of freedom. Our methodology and some results may be useful in the theory of Raman scattering and nuclear radiation. polar and two-polar (singular value) decompositions, dynamical affine invariance of equations of motion, mutual interaction between rotational and deformative degrees of freedom, lattice-like structures, quantum excitations of internal degrees of freedom, Raman-like phenomena. 1 Degrees of freedom, kinematical and canoni-cal variables, symmetries We can consider a system of material points, let us say physically a molecule or perhaps even the atomic nuclei, subject to translational motion, rigid rotations and homogeneous deformations. By this we mean that the current positions of constituent particles in the physical space, analytically speaking its Euler coordinates , are related to the reference Lagrange coordinates a K by the formula: