Geodesic
On the Lagrange-Souriau form in classical field theory
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 73-86

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MR Zbl
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-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.
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-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.
DOI : 10.21136/MB.1998.126290
Classification : 37J15, 37J99, 58F05, 70H03, 70H35, 70S05, 70S10
Keywords: Lagrangian formalism; classical field theory; Noetherian symmetries 
Grigore, D. R.; Popp, O. T. On the Lagrange-Souriau form in classical field theory. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 73-86. doi: 10.21136/MB.1998.126290
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