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On complexes related with calculus of variations

✍ Scribed by Hovhannes M. Khudaverdian; Theodore Voronov

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
244 KB
Volume
44
Category
Article
ISSN
0393-0440

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✦ Synopsis

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a particular new class of forms. We establish relation of the complex of variational derivatives and the variational complex. Certain calculus of Lagrangians of multidimensional paths is developed. It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes.

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