Applications of Dirac brackets to spinning particles

In a search for a classical antecedent of the Dirac equation, the author considers a series of Lagrangian models for spinning particles and derives the corresponding Hamiltonian theories. Most of these models involve the canonical quantization of a system with non-holonomic constraints. The author presents the constraints by Lagrange multipliers and Dirac's theory for singular Lagrangians is used to obtain the Hamiltonian theories. The Hamiltonian theories for the constrained systems allow a wider class of motions than the Lagrangian theory based on virtual displacements. A first-order relativistic wave equation is obtained involving operators associated wtih the Poincare group