The interior Euler-Lagrange operator in field theory

Year, pages: 2015, 1427 - 1444

The paper is devoted to the interior Euler-Lagrange operator in field theory, representing an important tool for constructing the variational sequence. We give a new invariant definition of this operator by means of a natural decomposition of spaces of differential forms, appearing in the sequence, which defines its basic properties. Our definition extends the well-known cases of the Euler-Lagrange class (Euler-Lagrange form) and the Helmholtz class (Helmholtz form). This linear operator has the property of a projector, and its kernel consists of contact forms. The result generalizes an analogous theorem valid for variational sequences over $1$-dimensional manifolds and completes the known heuristic expressions by explicit characterizations and proofs.

Volná, J., Urban, Z. 2015. The interior Euler-Lagrange operator in field theory. In Mathematica Slovaca, vol. 65, no.6, pp. 1427-1444. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0097

Volná, J., Urban, Z. (2015). The interior Euler-Lagrange operator in field theory. Mathematica Slovaca, 65(6), 1427-1444. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0097