nLab variational sequence



Variational calculus


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



Given a jet bundle J rEJ^r E of jets of finite order rr \in \mathbb{Z}, its variational sequence (Krupka 90) is a resolution of its constant sheaf of locally constant functions with values in the real numbers by a chain complex of quotient of sheaves of differential forms by combinations of contact forms and their de Rham differentials. (e.g. PRWM 15, section 2.2).

The variational sequence is a sub-sequence of the Euler complex as obtained from the theory of the variational bicomplex (Krupka 90, see e.g. PRWM 15,theorem 1).


The concept was introduced in

  • Demeter Krupka, Variational Sequences on Finite Order Jet Spaces, Proc. Diff. Geom. Appl.; J. Janyška, D. Krupka eds., World Sci. (Singapore, 1990) 236–254.

Review includes

  • Demeter Krupka, Introduction to Global Variational Geometry

  • M. Palese, O. Rossi, E. Winterroth, J. Musilova, Variational sequences, representation sequences and applications in physics (arXiv:1508.01752)

Last revised on July 24, 2022 at 18:40:08. See the history of this page for a list of all contributions to it.