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Conservation Laws and Their Application in Global Differential Geometry

In: Emmy Noether in Bryn Mawr

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  • Karen Uhlenbeck

    (University of Illinois, Department of Mathematics)

Abstract

Most of E. Noether’s mathematical research was in the field of algebra, or related to it. Outside this work in algebra is one very famous theorem of Noether’s which is stated in every book on classical mechanics, as well as in many texts on more recently developed physical theories [20]. This well-known theorem applies to the following situation: an (action) integral in the calculus of variations has continuous one-parameter groups of symmetries (or the infinitesimal version of these). Then Noether’s theorem states that to each such symmetry is associated a conservation law, or first integral† of the Euler-Lagrange equations for the integral.

Suggested Citation

  • Karen Uhlenbeck, 1983. "Conservation Laws and Their Application in Global Differential Geometry," Springer Books, in: Bhama Srinivasan & Judith D. Sally (ed.), Emmy Noether in Bryn Mawr, pages 103-115, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5547-5_6
    DOI: 10.1007/978-1-4612-5547-5_6
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