Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset; Pedro D. Prieto-Martínez; Narciso Román-Roy

Communications in Mathematics (2016)

  • Volume: 24, Issue: 2, page 137-152
  • ISSN: 1804-1388

Abstract

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The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.

How to cite

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Gaset, Jordi, Prieto-Martínez, Pedro D., and Román-Roy, Narciso. "Variational principles and symmetries on fibered multisymplectic manifolds." Communications in Mathematics 24.2 (2016): 137-152. <http://eudml.org/doc/287890>.

@article{Gaset2016,
abstract = {The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.},
author = {Gaset, Jordi, Prieto-Martínez, Pedro D., Román-Roy, Narciso},
journal = {Communications in Mathematics},
keywords = {Variational principles; Symmetries; Conserved quantities; Noether theorem; Fiber bundles; Multisymplectic manifolds; variational principles; symmetries; conserved quantities; Noether theorem; fiber bundles; multisymplectic manifolds.},
language = {eng},
number = {2},
pages = {137-152},
publisher = {University of Ostrava},
title = {Variational principles and symmetries on fibered multisymplectic manifolds},
url = {http://eudml.org/doc/287890},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Gaset, Jordi
AU - Prieto-Martínez, Pedro D.
AU - Román-Roy, Narciso
TI - Variational principles and symmetries on fibered multisymplectic manifolds
JO - Communications in Mathematics
PY - 2016
PB - University of Ostrava
VL - 24
IS - 2
SP - 137
EP - 152
AB - The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.
LA - eng
KW - Variational principles; Symmetries; Conserved quantities; Noether theorem; Fiber bundles; Multisymplectic manifolds; variational principles; symmetries; conserved quantities; Noether theorem; fiber bundles; multisymplectic manifolds.
UR - http://eudml.org/doc/287890
ER -

References

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