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The Euler-Lagrange expression and degenerate lagrange densities

Published online by Cambridge University Press:  09 April 2009

D. Lovelock
D. Lovelock
Affiliation:
Department of Applied MathematicsUniversity of WaterlooWaterloo, Ontario, Canada
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It is well known that many of the field equations from theoretical physics (e.g. Einstein field equations, Maxwell's equations, Klein-Gordon equation) can be obtained from a variational principle with a suitably chosen Lagrange density. In the case of the Einstein equations the corresponding Lagrangian is degenerate (i.e., the associated Euler-Lagrange equations are of second order whereas in general these would be of fourth order), while in the cases of the Maxwell and Klein-Gordon equations the Lagrangian usually used is not degenerate.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 482 - 495
Copyright
Copyright © Australian Mathematical Society 1972

References

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