MATHEMATICA BOHEMICA, Vol. 123, No. 1, pp. 73-86 (1998)

On the Lagrange-Souriau form
in classical field theory

D. R. Grigore, O. T. Popp

D. R. Grigore, O. T. Popp, Dept. of Theor. Phys., Inst. Atomic Phys., Bucharest-Magurele, P. O. Box MG 6, Romania, e-mail: grigore@theor1.ifa.ro, grigore@roifa.ifa.ro

Abstract: The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincaré-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to have a geometric point of view of the usual Noetherian symmetries for classical field theories and strongly supports the usefulness of the above mentioned differential form.

Keywords: Lagrangian formalism, classical field theory, Noetherian symmetries

Classification (MSC2000): 58F05, 70H35

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