Geodesic
General theory of Lie derivatives for Lorentz tensors
Communications in Mathematics, Tome 19 (2011) no. 1, pp. 11-25 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 14D21, 15A66, 22E70
Keywords: Lie derivative of spinors; Kosmann lift; Lorentz objects 
@article{COMIM_2011_19_1_a1,
     author = {Fatibene, Lorenzo and Francaviglia, Mauro},
     title = {General theory of {Lie} derivatives for {Lorentz} tensors},
     journal = {Communications in Mathematics},
     pages = {11--25},
     year = {2011},
     volume = {19},
     number = {1},
     mrnumber = {2855389},
     zbl = {1242.53053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2011_19_1_a1/}
}
TY  - JOUR
AU  - Fatibene, Lorenzo
AU  - Francaviglia, Mauro
TI  - General theory of Lie derivatives for Lorentz tensors
JO  - Communications in Mathematics
PY  - 2011
SP  - 11
EP  - 25
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2011_19_1_a1/
LA  - en
ID  - COMIM_2011_19_1_a1
ER  - 
%0 Journal Article
%A Fatibene, Lorenzo
%A Francaviglia, Mauro
%T General theory of Lie derivatives for Lorentz tensors
%J Communications in Mathematics
%D 2011
%P 11-25
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2011_19_1_a1/
%G en
%F COMIM_2011_19_1_a1
Fatibene, Lorenzo; Francaviglia, Mauro. General theory of Lie derivatives for Lorentz tensors. Communications in Mathematics, Tome 19 (2011) no. 1, pp. 11-25. http://geodesic.mathdoc.fr/item/COMIM_2011_19_1_a1/

[1] Barbero, F.: Real Ashtekar variables for Lorentzian signature space-time. Phys. Rev. D51 1996 5507–5510 | MR

[2] Bourguignon, J.-P., Gauduchon, P.: Spineurs, opérateurs de Dirac et variations de métriques. Commun. Math. Phys. 144 1992 581–599 | DOI | MR | Zbl

[3] Fatibene, L., Ferraris, M., Francaviglia, M.: Gauge formalism for general relativity and fermionic matter. Gen. Rel. Grav. 30 (9) 1998 1371–1389 | DOI | MR | Zbl

[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 | MR | Zbl

[5] Fatibene, L., Ferraris, M., Francaviglia, M., McLenaghan, R.G.: Generalized symmetries in mechanics and field theories. J. Math. Phys. 43 2002 3147–3161 | DOI | MR | Zbl

[6] Fatibene, L., Francaviglia, M.: Natural and Gauge Natural Formalism for Classical Field Theories. Kluwer Academic Publishers, Dordrecht 2003 xxii | MR | Zbl

[7] Fatibene, L., Francaviglia, M.: Deformations of spin structures and gravity. Acta Physica Polonica B 29 (4) 1998 915–928 | MR | Zbl

[8] Fatibene, L., Francaviglia, M., Rovelli, C.: On a Covariant Formulation of the Barbero-Immirzi Connection. Classical and Quantum Gravity 24 2007 3055–3066 | DOI | MR | Zbl

[9] Fatibene, L., Francaviglia, M., Rovelli, C.: Lagrangian Formulation of Ashtekar-Barbero-Immirzi Gravity. Classical and Quantum Gravity 24 2007 4207–4217 | DOI | MR

[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

[11] Figueroa-O’Farrill, J.M.: On the supersymmetries of anti de Sitter vacua. Classical and Quantum Gravity 16 1999 2043–2055 hep-th/9902066 | DOI | MR

[12] Godina, M., Matteucci, P.: The Lie derivative of spinor fields: theory and applications. Int. J. Geom. Methods Mod. Phys. 2 2005 159–188 math/0504366 | DOI | MR

[13] Holst, S.: Barbero’s Hamiltonian Derived from a Generalized Hilbert-Palatini Action. Phys. Rev. D53 1996 5966–5969 | MR

[14] Hurley, D.J., Vandyck, M.A.: On the concept of Lie and covariant derivatives of spinors, Part I. J. Phys. A 27 1994 4569–4580 | DOI | MR

[15] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag, N.Y. 1993 | MR

[16] Kosmann, Y.: Dérivées de Lie des spineurs. Ann. di Matematica Pura e Appl. 91 1972 317–395 | DOI | MR | Zbl

[17] Kosmann, Y.: Dérivées de Lie des spineurs. Comptes Rendus Acad. Sc. Paris, série A 262 1966 289–292 | MR | Zbl

[18] Kosmann, Y.: Dérivées de Lie des spineurs. Applications. Comptes Rendus Acad. Sc. Paris, série A 262 1966 394–397 | MR | Zbl

[19] Kosmann, Y.: Propriétés des dérivations de l’algèbre des tenseurs-spineurs. Comptes Rendus Acad. Sc. Paris, série A 264 1967 355–358 | MR

[20] Immirzi, G.: Quantum Gravity and Regge Calculus. Nucl. Phys. Proc. Suppl. 57 1997 65–72 | DOI | MR | Zbl

[21] Obukhov, Y.N., Rubilar, G.F.: Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry. Phys. Rev. D 74 2006 064002 gr-qc/0608064 | DOI

[22] Ortin, T.: A Note on Lie-Lorentz Derivatives. Classical and Quantum Gravity 19 2002 L143–L150 hep-th/0206159 | MR | Zbl

[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 | MR | Zbl

[25] Vandyck, M.A.: On the problem of space-time symmetries in the theory of supergravity. Gen. Rel. Grav. 20 1988 261–277 | DOI | Zbl

[26] Vandyck, M.A.: On the problem of space-time symmetries in the theory of supergravity, Part II. Gen. Rel. Grav. 20 1988 905–925 | DOI

[27] Yano, K.: The theory of Lie derivatives and its applications. North-Holland, Amsterdam 1955