Differential Geometric Aspects of the Cartan Form: Symmetry Theory

Document Type

Article

Publication Date

1-1-1987

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

This paper demonstrates that the classical Cartan form θ1L is not adequate for the determination of all the natural symmetries and conservation laws for a Lagrangian L. It is shown that the various extensions θ2L,..., θrL of the classical Cartan form, introduced in recent papers, give larger symmetry groups: G1⊆G2⊆⋅⋅⋅⊆Gr. This paper also introduces the notion of contact equivalent Lagrangians, which serves to clarify the idea that different Lagrangians can give rise to the same variational and symmetry theories.

Publication Title

Journal of Mathematical Physics

Volume

28

Issue

10

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