Poincaré gauge gravity: Selected topics

International Journal of Geometric Methods in Modern Physics

Volumn 3, Issue 1, 2006, Pages 95-137

  Obukhov, Yuri N ^a,b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Double duality; Gauge gravity; Spin; Torsion

Indexed keywords

EID: 33746300885     PISSN: 02198878     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021988780600103X     Document Type: Article

References (58)

1. M. Blagojević, Gravitation and Gauge Symmetries (IOP Publishing, Bristol, 2002).
2. F. W. Hehl, P. von der Heyde, G. D. Kerlick and J. M. Nester, General relativity with spin and torsion: Foundation and prospects, Revs. Mod. Phys. 48 (1976) 393-416.
3. F. W. Hehl, J. D. McCrea, E. W. Mielke and Y. Ne'eman, Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilaton invariance, Phys. Rep. 258 (1995) 1-171.
4. F. W. Hehl, J. Nitsch and P. von der Heyde, Gravitation and the Poincaré gauge field theory with quadratic Lagrangians, in General Relativity and Gravitation: One Hundred Years after the Birth of Albert Einstein, Vol. 1, ed. A. Held (Plenum, New York, 1980), pp. 329-355.
5. D. D. Ivanenko, P. I. Pronin and G. A. Sardanashvily, Gauge Theory of Gravity (Moscow University Publ. House, Moscow, 1985), p. 144 (in Russian).
6. D. Ivanenko and G. Sardanashvily, The gauge treatment of gravity, Phys. Rep. 94 (1983) 3-45.
7. J. D. McCrea, Reduce in general relativity and Poincarè gauge theory, in Algebraic Computing in General Relativity, Lect. Notes of the 1st Brasil. School on Comp. Algebra, Rio de Janeiro, July-August 1989, eds. M. J. Reboucas and W. L. Roque (Clarendon Press, Oxford, 1994), pp. 173-263.
8. E. W. Mielke, Geometrodynamics of Gauge Fields - On the Geometry of Yang-Mills and Gravitational Gauge Theories (Akademie Verlag, Berlin, 1987).
9. V. N. Ponomariev, A. O. Barvinsky and Yu. N. Obukhov, Geometrodynamical Methods and the Gauge Approach to the Theory of Gravitational Interactions (Energoatomizdat, Moscow, 1985), p. 168 (in Russian).
10. G. Sardanashvily and O. Zakharov, Gauge Gravitation Theory (World Scientific, Singapore, 1992).
11. I. L. Shapiro, Physical aspects of the space-time torsion, Phys. Rep. 357 (2002) 113-213.
12. A. Trautman, Recent advances in the Einstein-Cartan theory of gravity, Ann. N. Y. Acad. Sci. 262 (1975) 241-245.
13. A. Trautman, Fiber bundles, gauge fields and gravitation, in General Relativity and Gravitation: One Hundred Years after the Birth of Albert Einstein, Vol. 1, ed. A. Held (Plenum, New York, 1980), pp. 287-308.
14. A. Trautman, Differential Geometry for Physicists (Bibliopolis, Naples, 1984).
15. A. A. Tseytlin, Poincaré and de Sitter gauge theories of gravity with propagating torsion, Phys. Rev. D26 (1982) 3327-3341.
16. R. Tresguerres and E. W. Mielke, Gravitational Goldstone fields from affine gauge theory, Phys. Rev. D62 (2000) 044004 (7 pages).
17. R. Percacci, Geometry of Nonlinear Field Theories (World Scientific, Singapore, 1986), p. 255.
18. B. N. Frolov, Tetrad Palatini formalism and quadratic Lagrangians in the gravitational field theory, Acta Phys. Pol. B9 (1978) 823-829.
19. M. O. Katanaev, Kinematic part in the dynamical torsion theory, Theor. Math. Phys. 72 (1987) 735-741 [Theor. Math. Phys. 72 (1987) 79-88 (in Russian)].
20. W. Szczyrba, Dynamics of quadratic Lagrangians in gravity. Fairchild's theory, Contemp. Math. 71 (1988) 167-180.
21. F. W. Hehl, A. Macías, E. W. Mielke and Yu. N. Obukhov, On the structure of the energy-momentum and the spin currents in Dirac's electron theory, in On Einstein's Path, Essays in Honor of E. Schucking, ed. A. Harvey (Springer, New York, 1998), pp. 257-274.
22. Yu. N. Obukhov, On gravitational interaction of fermions, Fortschritte er Phys. 50 (2002) 711-716.
23. F. W. Hehl and Yu. N. Obukhov, Foundations of Classical Electrodynamics - Charge, Flux, and Metric (Birkhäuser, Boston, 2003).
24. R. Kuhfuss and J. Nitsch, Propagating modes in gauge field theories of gravity, Gen. Relat. Grav. 18 (1986) 1207-1227.
25. D. E. Neville, Gravity theories with propagating torsion, Phys. Rev. D21 (1980) 867-873.
26. E. Sezgin and P. van Nieuwenhuizen, New ghost-free gravity Lagrangians with propagating torsion, Phys. Rev. D21 (1980) 3269-3280.
27. E. Sezgin, A class of ghost-free gravity Lagrangians with massive or massless propagating torsion, Phys. Rev. D24 (1981) 1677-1680.
28. Yu. N. Obukhov, V. N. Ponomariev and V. V. Zhytnikov, Quadratic Poincaré gauge theory of gravity: A comparison with the general relativity theory, Gen. Relat. Grav. 21 (1989) 1107-1142.
29. R. D. Hecht, J. Lemke and R. P. Wallner, Can Poincaré gauge theory be saved? Phys. Rev. D44 (1991) 2442-2451.
30. W. Kopczyński, Problems with metric-teleparallel theories of gravitation, J. Phys. A15 (1982) 493-506.
31. J. M. Nester, Is there really a problem with the teleparallel theory? Class. Quantum Grav. 5 (1988) 1003-1010.
32. M. Leclerc, Teleparallel limit of Poincaré gauge theory, Phys. Rev. D71 (2005) 027503.
33. M. Leclerc, One-parameter teleparallel limit of Poincaré gravity, Phys. Rev. D72 (2005) 044002.
34. V. V. Zhytnikov, Double duality and hidden gauge freedom in the Poincaré gauge theory of gravitation, Gen. Rel. Grav. 28 (1996) 137-162.
35. P. Baekler, Prolongation structure and Backlund transformations of gravitational double duality equations, Class. Quantum Grav. 8 (1991) 1023-1046.
36. P. Baekler and F. W. Hehl, On the dynamics of the torsion of space-time: Exact solutions in a gauge theoretical model of gravity, in From SU(3) to Gravity. Festschrift in Honor of Y. Ne'eman, eds. E. Gotsman and G. Tauber (Cambridge University Press, Cambridge, 1985), pp. 341-359.
37. P. Baekler, F. W. Hehl and H. J. Lenzen, Vacuum solutions with double duality properties of the Poincaré gauge field theory II, in Proc. 3rd Marcel Grossmann Meeting on General Relativity, ed. Hu Ning (North Holland, Amsterdam, 1983), pp. 107-128.
38. P. Baekler, F. W. Hehl and E. W. Mielke, Vacuum solutions with double duality properties of a quadratic Poincaré gauge field theory, in Proc. 2nd Marcel Grossmann Meeting on Recent Progress of the Fundamentals of General Relativity, ed. R. Ruffini (North Holland, Amsterdam, 1981), pp. 413-450.
39. P. Baekler and E. W. Mielke, Effective Einsteinian gravity from Poincaré gauge field theory, Phys. Lett. A113 (1986) 471-475.
40. P. Baekler and E. W. Mielke, Hamiltonian structure of the Poincaré gauge theory and separation of non-dynamical variables in exact torsion solutions, Fortschr. Phys. 36 (1988) 549-594.
41. P. Baekler, E. W. Mielke, R. Hecht and F. W. Hehl, Kinky torsion in a Poincaré gauge model of gravity coupled to a massless scalar field, Nucl. Phys. B288 (1987) 800-812.
42. I. M. Benn, T. Dereli and R. W. Tucker, Double-dual solutions of generalized theories of gravitation, Gen. Relat. Grav. 13 (1981) 581-589.
43. E. W. Mielke, Reduction of the Poincaré gauge field equations by means of duality rotations, J. Math. Phys. 25 (1984) 663-668.
44. E. W. Mielke, On pseudoparticle solutions in the Poincaré gauge theory of gravity, Fortschr. Phys. 32 (1984) 639-660.
45. E. W. Mielke and R. P. Wallner, Mass and spin of double dual solutions in Poincaré gauge theory, Nuovo Cim. B101 (1988) 607-624.
46. 4 gravity. I. The ansatz for self double duality curvature, Gen. Relat. Grav. 23 (1991) 623-639.
47. j and spherically symmetric solutions to its field equations, in On Relativity Theory. Proc. of Sir A. Eddington Centenary Symp. Vol. 2, eds. Y. Choquet-Bruhat and T. M. Karade (World Scientific, Singapore, 1985), pp. 232-260.
48. M. S. Gladchenko and V. V. Zhytnikov, Post-Newtonian effects in the quadratic Poincaré gauge theory of gravitation, Phys. Rev. D50 (1994) 5060-5071.
49. J. D. McCrea, The use of REDUCE in finding exact solutions of the quadratic Poincaré gauge field equations, in Classical General Relativity, eds. W. B. Bonnor, J. N. Islam, and M. A. H. MacCallum (Cambridge University Press, Cambridge, 1984), pp. 173-182.
50. J. D. McCrea, Poincaré gauge theory of gravitation: Foundations, exact solutions and computer algebra, in Proc. 14th Intern. Conf. on Differential Geometric Methods in Mathematical Physics, Salamanca, 1985, eds. P. L. Garcia and A. Pérez-Rendón, Lect. Notes Math. 1251 (1987) 222-237.
51. A. V. Minkevich, Problem of cosmological singularity and gauge theories of gravitation, Acta Phys. Pol. 29 (1998) 949-960.
52. 2 theory of gravity with torsion, Phys. Rev. D19 (1979) 2264-2267.
53. 2 theories with torsion, Gen. Relat. Grav. 14 (1982) 331-354.
54. 2 gravity, J. Math. Phys. 35 (1994) 6001-6017.
55. V. V. Zhytnikov and V. N. Ponomariev, On the equivalence of vacuum equations in quadratic gauge theory of gravity and in general relativity, in Probl. Theor. Grav. and Elem. Particles, Vol. 17 ed. K. P. Stanyukovich (Energoatomizdat, Moscow, 1986), pp. 93-101 (in Russian).
56. G. Debney, E. E. Fairchild Jr. and S. T. C. Siklos, Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation, Gen. Relat. Grav. 9 (1978) 879-887.
57. E. E. Fairchild Jr., Gauge theory of gravitation, Phys. Rev. D14 (1976) 384-391; (E) 3439.
58. E. E. Fairchild Jr., Yang-Mills formulation of gravitational dynamics, Phys. Rev. D16 (1977) 2438-2447.