General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene; Mauro Francaviglia

Communications in Mathematics (2011)

  • Volume: 19, Issue: 1, page 11-25
  • ISSN: 1804-1388

Abstract

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We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

How to cite

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Fatibene, Lorenzo, and Francaviglia, Mauro. "General theory of Lie derivatives for Lorentz tensors." Communications in Mathematics 19.1 (2011): 11-25. <http://eudml.org/doc/196496>.

@article{Fatibene2011,
abstract = {We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.},
author = {Fatibene, Lorenzo, Francaviglia, Mauro},
journal = {Communications in Mathematics},
keywords = {Lie derivative of spinors; Kosmann lift; Lorentz objects; Lie derivatives; Kosmann lift; Lorentz tensors; Lorentz vectors},
language = {eng},
number = {1},
pages = {11-25},
publisher = {University of Ostrava},
title = {General theory of Lie derivatives for Lorentz tensors},
url = {http://eudml.org/doc/196496},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Fatibene, Lorenzo
AU - Francaviglia, Mauro
TI - General theory of Lie derivatives for Lorentz tensors
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 1
SP - 11
EP - 25
AB - We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
LA - eng
KW - Lie derivative of spinors; Kosmann lift; Lorentz objects; Lie derivatives; Kosmann lift; Lorentz tensors; Lorentz vectors
UR - http://eudml.org/doc/196496
ER -

References

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  1. Barbero, F., Real Ashtekar variables for Lorentzian signature space-time, Phys. Rev. D51 1996 5507–5510 (1996) MR1338108
  2. Bourguignon, J.-P., Gauduchon, P., 10.1007/BF02099184, Commun. Math. Phys. 144 1992 581–599 (1992) Zbl0755.53009MR1158762DOI10.1007/BF02099184
  3. Fatibene, L., Ferraris, M., Francaviglia, M., 10.1023/A:1018852524599, Gen. Rel. Grav. 30 (9) 1998 1371–1389 (1998) Zbl0935.83019MR1640625DOI10.1023/A:1018852524599
  4. Fatibene, L., Ferraris, M., Francaviglia, M., Godina, M., A geometric definition of Lie derivative for Spinor Fields, , I. Kolář (ed.)Proceedings of 6th International Conference on Differential Geometry and its Applications, August 28–September 1, 1995 MU University, Brno, Czech Republic 1996 549–557 (1996) Zbl0858.53035MR1406374
  5. Fatibene, L., Ferraris, M., Francaviglia, M., McLenaghan, R.G., 10.1063/1.1469668, J. Math. Phys. 43 2002 3147–3161 (2002) Zbl1059.70021MR1902473DOI10.1063/1.1469668
  6. Fatibene, L., Francaviglia, M., Natural and Gauge Natural Formalism for Classical Field Theories, Kluwer Academic Publishers, Dordrecht 2003 xxii (2003) Zbl1138.81303MR2039451
  7. Fatibene, L., Francaviglia, M., Deformations of spin structures and gravity, Acta Physica Polonica B 29 (4) 1998 915–928 (1998) Zbl0988.83043MR1682316
  8. Fatibene, L., Francaviglia, M., Rovelli, C., 10.1088/0264-9381/24/11/017, Classical and Quantum Gravity 24 2007 3055–3066 (2007) Zbl1117.83009MR2330908DOI10.1088/0264-9381/24/11/017
  9. Fatibene, L., Francaviglia, M., Rovelli, C., 10.1088/0264-9381/24/16/014, Classical and Quantum Gravity 24 2007 4207–4217 (2007) MR2348375DOI10.1088/0264-9381/24/16/014
  10. Fatibene, L., McLenaghan, R.G., Smith, S., Separation of variables for the Dirac equation on low dimensional spaces, , Advances in general relativity and cosmology Pitagora, Bologna 2003 109–127 (2003) 
  11. Figueroa-O’Farrill, J.M., 10.1088/0264-9381/16/6/330, Classical and Quantum Gravity 16 1999 2043–2055 hep-th/9902066 (1999) MR1697126DOI10.1088/0264-9381/16/6/330
  12. Godina, M., Matteucci, P., 10.1142/S0219887805000624, Int. J. Geom. Methods Mod. Phys. 2 2005 159–188 math/0504366 (2005) MR2140175DOI10.1142/S0219887805000624
  13. Holst, S., Barbero’s Hamiltonian Derived from a Generalized Hilbert-Palatini Action, Phys. Rev. D53 1996 5966–5969 (1996) MR1388932
  14. Hurley, D.J., Vandyck, M.A., 10.1088/0305-4470/27/13/030, J. Phys. A 27 1994 4569–4580 (1994) MR1294959DOI10.1088/0305-4470/27/13/030
  15. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, N.Y. 1993 (1993) MR1202431
  16. Kosmann, Y., 10.1007/BF02428822, Ann. di Matematica Pura e Appl. 91 1972 317–395 (1972) Zbl0231.53065MR0312413DOI10.1007/BF02428822
  17. Kosmann, Y., Dérivées de Lie des spineurs, Comptes Rendus Acad. Sc. Paris, série A 262 1966 289–292 (1966) Zbl0136.18403MR0200837
  18. Kosmann, Y., Dérivées de Lie des spineurs. Applications, Comptes Rendus Acad. Sc. Paris, série A 262 1966 394–397 (1966) Zbl0136.18403MR0200838
  19. Kosmann, Y., Propriétés des dérivations de l’algèbre des tenseurs-spineurs, Comptes Rendus Acad. Sc. Paris, série A 264 1967 355–358 (1967) MR0212712
  20. Immirzi, G., 10.1016/S0920-5632(97)00354-X, Nucl. Phys. Proc. Suppl. 57 1997 65–72 (1997) Zbl0976.83504MR1480184DOI10.1016/S0920-5632(97)00354-X
  21. Obukhov, Y.N., Rubilar, G.F., 10.1103/PhysRevD.74.064002, Phys. Rev. D 74 2006 064002 gr-qc/0608064 (2006) DOI10.1103/PhysRevD.74.064002
  22. Ortin, T., A Note on Lie-Lorentz Derivatives, Classical and Quantum Gravity 19 2002 L143–L150 hep-th/0206159 (2002) Zbl1004.83037MR1921400
  23. Sharipov, R., A note on Kosmann-Lie derivatives of Weyl spinors, arXiv: 0801.0622 
  24. Trautman, A., Invariance of Lagrangian Systems, , Papers in honour of J. L. Synge Clarenden Press, Oxford 1972 85–100 (1972) Zbl0273.58004MR0503424
  25. Vandyck, M.A., 10.1007/BF00759185, Gen. Rel. Grav. 20 1988 261–277 (1988) Zbl0647.53074DOI10.1007/BF00759185
  26. Vandyck, M.A., 10.1007/BF00760090, Gen. Rel. Grav. 20 1988 905–925 (1988) DOI10.1007/BF00760090
  27. Yano, K., The theory of Lie derivatives and its applications, North-Holland, Amsterdam 1955 (1955) 

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