LATTICE-DYNAMICS SHELL-MODEL AS A CONSTRAINED HAMILTONIAN SYSTEM

The authors show that the shell model, currently used in the lattice dynamics study of ionic crystals, is a singular system. The model is treated as a constrained Hamiltonian system. The use of the Dirac generalized Hamiltonian formalism for constrained systems permits them to solve the difficulties which appear in quantum mechanics and statistical mechanics formulations. The constraints, first-class Hamiltonian and Dirac bracket are obtained. The general expression for the partition function of the quantum statistical mechanics is defined. Finally some considerations about the perturbative and non-perturbative methods are performed.