On finite order variational sequences

Details On finite order variational sequences On finite order variational sequences

2000-01-05

arxiv.org/abs/math-ph/0001009v1

Physics

Mathematical Physics

LaTeX2e with Paul Taylor's diagrams, 38 pages, no figures. Long version of a paper appeared in Math. Proc. Camb. Phil. Soc. 12

Scientific paper

We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present an intrinsic formulation for the Helmholtz condition of local variationality using a technique introduced by Kolar that we have adapted to our context. Finally, we provide the minimal order solution to the inverse problem of the calculus of variations and a solution of the problem of the variationally trivial Lagrangian.

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