Abstract
A novel analysis of the gauge theory of the local Lorentz group is implemented both in flat and in curved space-time, and the resulting dynamics is analyzed in view of the geometrical interpretation of the gauge potential. The Yang-Mills picture of local Lorentz transformations is first approached in a second-order formalism. For the Lagrangian approach to reproduce the second Cartan structure equation as soon as the Lorentz gauge connections are identified with the contortion tensor, an interaction term between the Lorentz gauge fields and the spin connections has to be postulated. The full picture involving gravity, torsion and spinors is described by a coupled set of field equations, which allows one to interpret both gravitational spin connections and matter spin density as the source term for the Yang-Mills equations. The contortion tensor acquires a propagating character, because of its non-Abelian feature, and the pure contact interaction is restored in the limit of vanishing Lorentz connections.
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References
R. Utiyama, Phys. Rev. 101, 1597 (1956)
T.W.B. Kibble, J. Math. Phys. 2, 212 (1961)
M. Blagojevic, Gravitation and Gauge Symmetries (IoP Publishing, 2002)
F.W. Hehl, P. von der Heyde, G.D. Kerlick, J. Nester, Rev. Mod. Phys. 48, 393 (1976)
F.W. Hehl, Gen. Relativ. Gravit. J. 4, 333 (1973)
F.W. Hehl, Gen. Relativ. Gravit. J. 5, 491 (1974)
F.W. Hehl, P. von der Heyde, G.D. Kerlick, Phys. Rev. D 10, 1066 (1974)
P. Von der Heyde, Phys. Lett. A 58, 141 (1976)
M. Blagojevic, SFIN A 1, 147 (2003) gr-qc/0302040
S. Deser, C.J. Isham, Phys. Rev. D 14, 2505 (1976)
J. Nitsch, in Proceedings of the 6th Course of the School of Cosmology and Gravitation on Spin, Torsion and Supergravity, Erice (Italy) 1979, edited by P.G. Bergmann, V. de Sabbata (Plenum Press, New York, 1980) p. 63
F.W. Hehl, in Proceedings of the 6th Course of the School of Cosmology and Gravitation on Spin, Torsion and Supergravity, Erice (Italy) 1979, edited by P.G. Bergmann, V. de Sabbata (Plenum Press, New York, 1980) p. 5
R. Wald, General Relativity (The University of Chicago Press, 1984)
A. Barducci, R. Casalbuoni, L. Lusanna, Nucl. Phys. B 124, 521 (1976)
A. Cant, Y. Ne'eman, J. Math. Phys. 26, 3180 (1985)
Y. Ne'eman, D. Sijacki, Found. Phys. 27, 1105 (1997) gr-qc/9804037
O.M. Lecian, S. Mercuri, in Proceedings of the 9th Marcel Grossmann Meeting, Berlin 2006 (World Scientific, 2008) p. 2668
F.W. Hehl, J.D. McCrea, E.W. Mielke, Y. Ne'eman, Phys. Rep. 258, 1 (1995)
Y.N. Obukhov, J.G. Pereira, Phys. Rev. D 76, 044016 (2003)
F. Gronwald, F.W. Hehl, On the Gauge Aspects of Gravity, in Proceedings of the 14th Course of the School of Cosmology and Gravitation, Erice (Italy) 1995 (World Scientific, Singapore, 1996)
F.W. Hehl, A. Macias, Int. J. Mod. Phys. D 8, 399 (1999)
N. Carlevaro, O.M. Lecian, G. Montani, Ann. Fond. L. de Broglie 32, 281 (2007)
N. Carlevaro, O.M. Lecian, G. Montani, Int. J. Mod. Phys. A 23, 1282 (2008)
G. Aprea, G. Montani, R. Ruffini, Int. J. Mod. Phys. D 12, 1875 (2003)
R. de Azeredo Campos, P.S. Letelier, Prog. Theor. Phys. 75, 1359 (1986)
H.J. Xie, T. Shirafuji, Prog. Theor. Phys. 97, 129 (1997)
K. Hayashi, T. Shirafuji, Prog. Theor. Phys. 64, 866 (1980)
K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979)
A. Tiemblo, R. Tresguerres, Eur. Phys. J. C 42, 437 (2005)
C. Wiesendanger, in Proceedings on ``Quantum Gravity'', Erice (Italy) 1995 (World Scientific, Singapore, 1996) gr-qc/9604043
C. Wiesendanger, Class. Quantum Grav. 13, 681 (1996)
K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979)
F.W. Hehl, J. Nitsch, P. von der Heyde, in General Relativity and Gravitation - One Hundred Years after the Birth of A. Einstein, edited by A. Held, Vol. 1 (Plenum, 1980) p. 329
J. Nitsch, in Cosmology and Gravitation - Spin, Torsion, Rotation and Supergravity, edited by P.G. Bergmann, V. de Sabbata (Plenum, 1980) p. 63
M. Blagojević, M. Vasilić, Class. Quantum Grav. 17, 3785 (2000)
W. Kopczyński, J. Phys. A 15, 493 (1982)
W.-H. Cheng, D.-C. Chern, J.M. Nester, Phys. Rev. D 38, 2656 (1988)
H. Chen, J.M. Nester, H.J. Yo, Acta Phys. Pol. B 29, 961 (1998)
M. Leclerc, Phys. Rev. D 71, 027503 (2005)
M. Leclerc, Phys. Rev. D 72, 044002 (2005)
F. Mandl, F. Shaw, Quantum Field Theory (J. Wiley and Sons, 1984)
S. Weinberg, The Quantum Theory of Fields (Cambridge University Press, 1995)
I.L. Shapiro, Phys. Rep. 357, 113 (2002)
T. Obata, Prog. Theor. Phys. 70, 622 (1983)
F. Bigazzi, L. Lusanna, Int. J. Mod. Phys. A 14, 1877 (1999)
A. Ashtekar, J.D. Romano, R.S. Tate, Phys. Rev. D 40, 2572 (1989)
S. Casanova, O.M. Lecian, G. Montani, R. Ruffini, R. Zalaletdinov, Mod. Phys. Lett. A 23, 17 (2008)
K. Hajashi, T. Shirafui, Prog. Theor. Phys. 64, 883 (1980)
K. Hajashi, T. Shirafui, Prog. Theor. Phys. 64, 1435 (1980)
R.T. Hammond, Rep. Prog. Phys. 65, 599 (2002)
S.M. Carroll, G.B. Field, Phys. Rev. D 50, 3867 (1994)
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Lecian, O.M., Montani, G. & Carlevaro, N. Novel analysis of spinor interactions and non-Riemannian geometry. Eur. Phys. J. Plus 128, 19 (2013). https://doi.org/10.1140/epjp/i2013-13019-y
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DOI: https://doi.org/10.1140/epjp/i2013-13019-y