Relations between constants of motion and conserved functions

Josef Janyška

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 5, page 297-313
  • ISSN: 0044-8753

Abstract

top
We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.

How to cite

top

Janyška, Josef. "Relations between constants of motion and conserved functions." Archivum Mathematicum 051.5 (2015): 297-313. <http://eudml.org/doc/276162>.

@article{Janyška2015,
abstract = {We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.},
author = {Janyška, Josef},
journal = {Archivum Mathematicum},
keywords = {phase space; infinitesimal symmetry; hidden symmetry; gravitational contact phase structure; almost-cosymplectic-contact phase structure; Killing multi-vector field; Killing–Maxwell multi-vector field; function constant of motions; conserved function},
language = {eng},
number = {5},
pages = {297-313},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Relations between constants of motion and conserved functions},
url = {http://eudml.org/doc/276162},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Janyška, Josef
TI - Relations between constants of motion and conserved functions
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 5
SP - 297
EP - 313
AB - We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.
LA - eng
KW - phase space; infinitesimal symmetry; hidden symmetry; gravitational contact phase structure; almost-cosymplectic-contact phase structure; Killing multi-vector field; Killing–Maxwell multi-vector field; function constant of motions; conserved function
UR - http://eudml.org/doc/276162
ER -

References

top
  1. Crampin, M., 10.1016/0034-4877(84)90069-7, Reports Math. Phys. 20 (1984), 31–40. DOI: http://dx.doi.org/10.1016/0034-4877(84)90069-7 (1984) Zbl0551.58019MR0761328DOI10.1016/0034-4877(84)90069-7
  2. Duval, C., Valent, G., 10.1063/1.1899986, J. Math. Phys. 46 (5) (2005), 053516. DOI: http://dx.doi.org/10.1063/1.1899986 (2005) Zbl1110.81116MR2143025DOI10.1063/1.1899986
  3. Iwai, T., Symmetries in relativistic dynamics of a charged particle, Ann. Inst. H. Poincaré Sect. A (N.S.) 25 (1976), 335–343. (1976) Zbl0339.53039MR0434248
  4. Janyška, J., 10.1063/1.4733369, AIP Conf. Proc. 1460, XX Internat. Fall Workshop on Geometry and Physics, 2011, pp. 135–140. DOI: http://dx.doi.org/10.1063/1.4733369 (2011) DOI10.1063/1.4733369
  5. Janyška, J., 10.5817/AM2014-5-297, Arch. Math. (Brno) 50 (5) (2014), 297–316. DOI: http://dx.doi.org/10.5817/AM2014-5-297 (2014) Zbl1340.70017MR3303779DOI10.5817/AM2014-5-297
  6. Janyška, J., 10.1142/S0219887814600202, Int. J. Geom. Methods Mod. Phys. 11 (7) (2014), 1460020. DOI: http://dx.doi.org/10.1142/S0219887814600202 (2014) MR3249642DOI10.1142/S0219887814600202
  7. Janyška, J., 10.1142/S0219887815600208, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1560020. DOI: http://dx.doi.org/10.1142/S0219887815600208 (2015) MR3400660DOI10.1142/S0219887815600208
  8. Janyška, J., Modugno, M., 10.1142/S021988780800303X, Int. J. Geom. Methods Mod. Phys. 5 (2008), 699–754. DOI: http://dx.doi.org/10.1142/S021988780800303X (2008) Zbl1160.53008MR2445392DOI10.1142/S021988780800303X
  9. Janyška, J., Modugno, M., 10.1016/j.matpur.2008.09.007, J. Math. Pures Appl. (9) 91 (2009), 211–2332. DOI: http://dx.doi.org/10.1016/j.matpur.2008.09.007 (2009) Zbl1163.53051MR2498755DOI10.1016/j.matpur.2008.09.007
  10. Janyška, J., Modugno, M., Vitolo, R., 10.1007/s10440-009-9505-6, Acta Appl. Math. 110 (2010), 1249–1276. DOI: http://dx.doi.org/10.1007/s10440-009-9505-6 (2010) Zbl1208.15021MR2639169DOI10.1007/s10440-009-9505-6
  11. Janyška, J., Vitolo, R., 10.1088/1751-8113/45/48/485205, J. Phys. A: Math. Theor. 45 (2012), 485205. DOI: http://dx.doi.org/10.1088/1751-8113/45/48/485205 (2012) Zbl1339.70036MR2998421DOI10.1088/1751-8113/45/48/485205
  12. Olver, P., 10.1007/978-1-4684-0274-2_2, Graduate Texts in Mathematics, vol. 107, Springer, 1986. (1986) Zbl0588.22001MR0836734DOI10.1007/978-1-4684-0274-2_2
  13. Sommers, P., 10.1063/1.1666395, J. Math. Phys. 14 (1973), 787–790. DOI: http://dx.doi.org/10.1063/1.1666395 (1973) MR0329558DOI10.1063/1.1666395

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.