Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be written as a density on a suitable “covariant prolongation bundle”; the related momenta turn out to be natural vector- valued forms, and the field equations can be expressed in terms of covariant exterior differentials of the momenta. Currents and energy-tensors naturally also fit into this formalism. The examples of bosonic fields and spin one-half fields, interacting with non- Abelian gauge fields, are worked out. The “metric-affine” description of the gravitational field is naturally included, too.
Covariant-differential formulation of Lagrangian field theory / Daniel Canarutto. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - STAMPA. - 15:(2018), pp. 1-23. [10.1142/S0219887818501335]
Covariant-differential formulation of Lagrangian field theory
Daniel Canarutto
2018
Abstract
Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be written as a density on a suitable “covariant prolongation bundle”; the related momenta turn out to be natural vector- valued forms, and the field equations can be expressed in terms of covariant exterior differentials of the momenta. Currents and energy-tensors naturally also fit into this formalism. The examples of bosonic fields and spin one-half fields, interacting with non- Abelian gauge fields, are worked out. The “metric-affine” description of the gravitational field is naturally included, too.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.