On the Lagrange-Souriau form in classical field theory

D. R. Grigore; Octavian T. Popp

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 1, page 73-86
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Grigore, D. R., and Popp, Octavian T.. "On the Lagrange-Souriau form in classical field theory." Mathematica Bohemica 123.1 (1998): 73-86. <http://eudml.org/doc/248311>.

@article{Grigore1998,
abstract = {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.},
author = {Grigore, D. R., Popp, Octavian T.},
journal = {Mathematica Bohemica},
keywords = {Lagrangian formalism; classical field theory; Noetherian symmetries; Lagrangian formalism; classical field theory; Noetherian symmetries},
language = {eng},
number = {1},
pages = {73-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Lagrange-Souriau form in classical field theory},
url = {http://eudml.org/doc/248311},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Grigore, D. R.
AU - Popp, Octavian T.
TI - On the Lagrange-Souriau form in classical field theory
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 1
SP - 73
EP - 86
AB - 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.
LA - eng
KW - Lagrangian formalism; classical field theory; Noetherian symmetries; Lagrangian formalism; classical field theory; Noetherian symmetries
UR - http://eudml.org/doc/248311
ER -

References

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