Dirac constraints in field theory and exterior differential systems

• Autores: Capriotti, Santiago
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Dirac Constraints; Exterior Differential Systems; Classical Field Theory
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the jet variables. So it is natural to ask if there exists a formulation of this kind of field theories which avoids this problem, retaining the versatility of the known approach. The following paper deals with a family of variational problems, namely, the so called non standard variational problems, which intends to capture the data necessary to set up such a formulation for field theories. A multisymplectic structure for the family of non standard variational problems will be found, and it will be related with the (pre)symplectic structure arising on the space of sections of the bundle of fields. In this setting the Dirac theory of constraints will be studied, obtaining among other things a novel characterization of the constraint manifold which arises in this theory, as generators of an exterior differential system associated to the equations of motion and the chosen slicing. Several examples of application of this formalism will be discussed.
Fil: Capriotti, Santiago. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina