An invariance theory for second-order variational problems
- 1 July 1975
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 16 (7) , 1374-1379
- https://doi.org/10.1063/1.522706
Abstract
This paper investigates the invariance properties of second‐order variational problems when the configuration space is subjected to an r‐parameter local Lie group of transformations. In particular, the recent results of Hanno Rund on first‐order problems are extended to the higher order case: A new set of fundamental invariance identities are derived for single and multiple integral problems, and new proofs of the Zermelo conditions and Noether’s theorem are presented. The results are applied to a variational problem whose second‐order Lagrangian depends upon a scalar field in Minkowski space, and some conformal identities are obtained.Keywords
This publication has 4 references indexed in Scilit:
- Conformal invariance of multiple integrals in the calculus of variationsJournal of Mathematical Analysis and Applications, 1974
- Invariance and the n-body problemJournal of Mathematical Analysis and Applications, 1973
- Noether's theorem in generalized mechanicsJournal of Physics A: Mathematical, Nuclear and General, 1973
- The theory of problems in the calculus of variations whose Lagrangian function involves second order derivatives: A new approachAnnali di Matematica Pura ed Applicata (1923 -), 1961