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Symmetries, conservation laws and variational principles for vector field theories†

Published online by Cambridge University Press:  24 October 2008

Ian M. Anderson  and
Juha Pohjanpelto
Ian M. Anderson
Affiliation:
Department of Mathematics, Utah State University, Logan, Utah, 84322–3900, U.S.A.
Juha Pohjanpelto
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331–4605, U.S.A.
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Extract

The interplay between symmetries, conservation laws, and variational principles is a rich and varied one and extends well beyond the classical Noether's theorem. Recall that Noether's first theorem asserts that to every r dimensional Lie algebra of (generalized) symmetries of a variational problem there are r conserved quantities for the corresponding Euler-Lagrange equations. Noether's second theorem asserts that infinite dimensional symmetry algebras (depending upon arbitrary functions of all the independent variables) lead to differential identities for the Euler-Lagrange equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 2 , August 1996 , pp. 369 - 384
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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