Varational Equations and Symmetries in the Lagrangian Formalism
D. R. Grigore
Abstract
Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the second order derivatives. This structure can be used to make more precise the form of a general symmetry. As an illustration we analyse the case of Lagrangian equations with Poincaré invariance or with universal invariance.
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