Lepage forms theory applied

Michal Lenc; Jana Musilová; Lenka Czudková

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 4, page 279-287
  • ISSN: 0044-8753

Abstract

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In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example.

How to cite

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Lenc, Michal, Musilová, Jana, and Czudková, Lenka. "Lepage forms theory applied." Archivum Mathematicum 045.4 (2009): 279-287. <http://eudml.org/doc/250692>.

@article{Lenc2009,
abstract = {In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example.},
author = {Lenc, Michal, Musilová, Jana, Czudková, Lenka},
journal = {Archivum Mathematicum},
keywords = {fibred manifold; Lagrangian; Lepage form; conservation laws; relativistic mechanics; fibred manifold; Lagrangian; Lepage form; conservation law; relativistic mechanics},
language = {eng},
number = {4},
pages = {279-287},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lepage forms theory applied},
url = {http://eudml.org/doc/250692},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Lenc, Michal
AU - Musilová, Jana
AU - Czudková, Lenka
TI - Lepage forms theory applied
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 4
SP - 279
EP - 287
AB - In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example.
LA - eng
KW - fibred manifold; Lagrangian; Lepage form; conservation laws; relativistic mechanics; fibred manifold; Lagrangian; Lepage form; conservation law; relativistic mechanics
UR - http://eudml.org/doc/250692
ER -

References

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  1. Krupka, D., Global variational theory in fibred spaces, Handbook of global analysis (Krupka, D., Saunders, D., eds.), Elsevier, 2007, pp. 773–836. (2007) MR2389646
  2. Krupková, O., 10.1063/1.532196, J. Math. Phys. 38 (1997), 5098–5126. (1997) MR1471916DOI10.1063/1.532196
  3. Krupková, O., The Geometry of Ordinary Variational Equations, Lecture Notes in Math., vol. 1678, Springer, Berlin, 1997. (1997) MR1484970
  4. Krupková, O., Musilová, J., 10.1088/0305-4470/34/18/313, J. Phys. A: Math. Gen. 34 (2001), 3859–3875. (2001) MR1840850DOI10.1088/0305-4470/34/18/313
  5. Musilová, J., Lenc, M., Lepage forms in variational theories: From Lepage’s idea to the variational sequence, Variations, Geometry and Physics (2008), 1–31, O. Krupková and D. Saunders (Editors). Nova Science Publishers. (2008) MR2523430
  6. Weinberg, S., Cosmology, Oxford University Press, 2008. (2008) Zbl1147.83002MR2410479

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