Previous |  Up |  Next

Article

Keywords:
Lie derivative of spinors; Kosmann lift; Lorentz objects
Summary:
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.
References:
[1] Barbero, F.: Real Ashtekar variables for Lorentzian signature space-time. Phys. Rev. D51 1996 5507–5510 MR 1338108
[2] Bourguignon, J.-P., Gauduchon, P.: Spineurs, opérateurs de Dirac et variations de métriques. Commun. Math. Phys. 144 1992 581–599 DOI 10.1007/BF02099184 | MR 1158762 | Zbl 0755.53009
[3] Fatibene, L., Ferraris, M., Francaviglia, M.: Gauge formalism for general relativity and fermionic matter. Gen. Rel. Grav. 30 (9) 1998 1371–1389 DOI 10.1023/A:1018852524599 | MR 1640625 | Zbl 0935.83019
[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 1406374 | Zbl 0858.53035
[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 10.1063/1.1469668 | MR 1902473 | Zbl 1059.70021
[6] Fatibene, L., Francaviglia, M.: Natural and Gauge Natural Formalism for Classical Field Theories. Kluwer Academic Publishers, Dordrecht 2003 xxii MR 2039451 | Zbl 1138.81303
[7] Fatibene, L., Francaviglia, M.: Deformations of spin structures and gravity. Acta Physica Polonica B 29 (4) 1998 915–928 MR 1682316 | Zbl 0988.83043
[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 10.1088/0264-9381/24/11/017 | MR 2330908 | Zbl 1117.83009
[9] Fatibene, L., Francaviglia, M., Rovelli, C.: Lagrangian Formulation of Ashtekar-Barbero-Immirzi Gravity. Classical and Quantum Gravity 24 2007 4207–4217 DOI 10.1088/0264-9381/24/16/014 | MR 2348375
[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 10.1088/0264-9381/16/6/330 | MR 1697126
[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 10.1142/S0219887805000624 | MR 2140175
[13] Holst, S.: Barbero’s Hamiltonian Derived from a Generalized Hilbert-Palatini Action. Phys. Rev. D53 1996 5966–5969 MR 1388932
[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 10.1088/0305-4470/27/13/030 | MR 1294959
[15] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag, N.Y. 1993 MR 1202431
[16] Kosmann, Y.: Dérivées de Lie des spineurs. Ann. di Matematica Pura e Appl. 91 1972 317–395 DOI 10.1007/BF02428822 | MR 0312413 | Zbl 0231.53065
[17] Kosmann, Y.: Dérivées de Lie des spineurs. Comptes Rendus Acad. Sc. Paris, série A 262 1966 289–292 MR 0200837 | Zbl 0136.18403
[18] Kosmann, Y.: Dérivées de Lie des spineurs. Applications. Comptes Rendus Acad. Sc. Paris, série A 262 1966 394–397 MR 0200838 | Zbl 0136.18403
[19] Kosmann, Y.: Propriétés des dérivations de l’algèbre des tenseurs-spineurs. Comptes Rendus Acad. Sc. Paris, série A 264 1967 355–358 MR 0212712
[20] Immirzi, G.: Quantum Gravity and Regge Calculus. Nucl. Phys. Proc. Suppl. 57 1997 65–72 DOI 10.1016/S0920-5632(97)00354-X | MR 1480184 | Zbl 0976.83504
[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 10.1103/PhysRevD.74.064002
[22] Ortin, T.: A Note on Lie-Lorentz Derivatives. Classical and Quantum Gravity 19 2002 L143–L150 hep-th/0206159 MR 1921400 | Zbl 1004.83037
[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 0503424 | Zbl 0273.58004
[25] Vandyck, M.A.: On the problem of space-time symmetries in the theory of supergravity. Gen. Rel. Grav. 20 1988 261–277 DOI 10.1007/BF00759185 | Zbl 0647.53074
[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 10.1007/BF00760090
[27] Yano, K.: The theory of Lie derivatives and its applications. North-Holland, Amsterdam 1955
Partner of
EuDML logo