On the gauge structure of the calculus of variations with constraints

Details On the gauge structure of the calculus of variations with constraints On the gauge structure of the calculus of variations with constraints

2011-01-26

arxiv.org/abs/1101.5045v1

Physics

Mathematical Physics

21 pages

Scientific paper

A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the Lagrangian is replaced by a section of a suitable principal fibre bundle over the velocity space. A geometric rephrasement of Pontryagin's maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved.

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