Abstract
The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by the traditional formalisms. Any spin-affine connexion appears to possess a torsional part which is conveniently chosen as a suitable asymmetric contribution. Such a torsional affine contribution thus supplies a gauge-invariant potential that can eventually be taken to carry an observable character, and thereby effectively takes over the role of any trivially realizable symmetric contribution. The overall curvature spinors for any spin-affine connexion accordingly emerge from the irreducible decomposition of a mixed world-spin object which in turn comes out of the action on elementary spinors of a typical torsionful second-order covariant derivative operator. Explicit curvature expansions are likewise exhibited which fill in the gap related to their absence from the literature. It is then pointed out that the utilization of the torsionful spinor framework may afford locally some new physical descriptions.
Similar content being viewed by others
References
A. Trautman, Encyclopedia of Mathematical Physics, edited by J.P. Françoise, G.L. Naber, S.T. Tsou, Vol. 2 (Elsevier, Oxford, 2006) p. 189.
S. Capozziello et al., Int. J. Geom. Methods Mod. Phys. 5, 765 (2008).
F.W. Hehl et al., Rev. Mod. Phys. 48, 393 (1976).
R. Penrose, W. Rindler, Spinors and Space-Time, Vol. 1 (Cambridge University Press, 1984).
T.W. Kibble, J. Math. Phys. 2, 212 (1961).
D.W. Sciama, On the Analogy Between Charge and Spin in General Relativity, in Recent Developments in General Relativity (Pergamon and PWN, Oxford, 1962).
S. Vignolo, L. Fabbri, Int. J. Geom. Methods Mod. Phys. 9, 1250054 (2012).
S. Capozziello et al., Class. Quantum Grav. 24, 6417 (2007).
N.J. Poplawski, Phys. Lett. B 694, 181 (2010).
L. Fabbri, S. Vignolo, Int. J. Theor. Phys. 51, 3186 (2012).
L.H. Ryder, I.L. Shapiro, Phys. Lett. A 247, 21 (1998).
V. De Sabbata, C. Sivaram, Astrophys. Space Sci. 158, 347 (1989).
S. Capozziello et al., Eur. Phys. J. C 72, 1908 (2012).
T.P. Sotiriou, S. Liberati, Ann. Phys. 322, 935 (2007).
T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).
L. Infeld, B.L. Van der Waerden, Sitzber. Akad. Wiss., Physik-math. Kl. 9, 380 (1933).
H. Weyl, Z. Phys. 56, 330 (1929).
J.G. Cardoso, Czech J. Phys. 4, 401 (2005).
J.G. Cardoso, Adv. Appl. Clifford Algebras 22, 985 (2012).
R. Penrose, Ann. Phys. 10, 171 (1960).
L. Witten, Phys. Rev. 1, 357 (1959).
J.G. Cardoso, Acta Phys. Pol. 38, 2525 (2007).
J.G. Cardoso, Nuovo Cimento B 124, 631 (2009).
J. G. Cardoso, Wave Equations for Invariant Infeld-van der Waerden Wave Functions for Photons and Their Physical Significance, in Photonic Crystals: Optical Properties, Fabrication , editid by William L. Dahl (Nova Science Publishers, Inc., 2010) ISBN: 978-1-61122-413-9.
H. Jehle, Phys. Rev. 75, 1609 (1949).
W.L. Bade, H. Jehle, Rev. Mod. Phys. 25, 714 (1953).
P.G. Bergmann, Phys. Rev. 107, 624 (1957).
E.T. Newman, R. Penrose, J. Math. Phys. 3, 566 (1962).
R. Penrose, W. Rindler, Spinors and Space-Time, Vol. 2 (Cambridge University Press, 1986).
J. Plebanski, Acta Phys. Pol. 27, 361 (1965).
R. Penrose, Found. Phys. 13, 325 (1983).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cardoso, J.G. Two-component spinors in spacetimes with torsionful affinities. Eur. Phys. J. Plus 130, 10 (2015). https://doi.org/10.1140/epjp/i2015-15010-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2015-15010-0