EXTERIOR DIFFERENTIAL SYSTEM AND THE DIRAC THEORY OF CONSTRAINTS

SANTIAGO CAPRIOTTI

Santiago de Compostela

Encuentro; First Iberoamerican Meeting of Geometry, Mechanics and Control; 2008

Universidad de Santiago de Compostela - Consejo Superior de Investigaciones Científicas de España

We try to understand the way in which arise the constraints in the analysis of singular eld theories through the Dirac method. To this end, we formulate the equations of motion as a variational problem, whose extremals are caracterized as integral submanifold of an exterior dierential system (EDS); in this way we obtain conditions that ensures the existence of such submanifolds, through the Cartan-Kähler theorem. We nd a multisymplectic version for this system, by applying a generalization of the corresponding method in classical mechanics [H]; finally we apply this scheme in order to establish a relation between the conditions for the fields arising via the Dirac algorithm [G], with the integrability conditions that follows from the Cartan-Kähler theorem. References [H] D Hartley, R W Tucker and P A Tuckey, Constrained dynamics and exterior differential systems, J. Phys. A: Math. Gen. 24 5253-5265, 1991. [G] Gotay M., unpublished notes.