Abstract
Since the work of Lagrange, it is well known that the equations of classical mechanics can be obtained as solutions of a variational problem, using a suitable functional, called the action on the configuration space (cf. [Ab-Ma], [Arn]). Hilbert proved ([Hil]) that the equations of general relativity can be recovered from the action (math) (total scalar curvature). His paper contains prophetic ideas about the role played by the diffeomorphism group, which he already considered as a “gauge group”.
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© 1987 Springer-Verlag Berlin Heidelberg
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Besse, A.L. (1987). Riemannian Functionals. In: Einstein Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74311-8_5
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DOI: https://doi.org/10.1007/978-3-540-74311-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74120-6
Online ISBN: 978-3-540-74311-8
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