Noether symmetries and conserved momenta of Dirac equation in presymplectic dynamics.

ABSTRACT: Presymplectic dynamics, as it arises from the Lagrangian and Hamiltonian dynamics of non-regular mechanical systems, has proved to be a theory whose focus is an implicit differential equation called Dirac equation [3]. A general geometric framework developped for implicit differential equations [4] will be applied to Dirac equation, with the aim of gaining a clear understanding of its possible symmetries and their role in the problem of integration. Noether's theory of symmetries and conserved momenta will then be extended to Dirac equation, and thence to non-regular Lagrangian and Hamiltonian dynamics. The overall picture will appear to be the most natural generalization of the classical theory concerning regular mechanical systems.