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Four Lectures on Poincaré Gauge Field Theory

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Cosmology and Gravitation

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 58))

Abstract

The Poincaré (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincaré group. The physical laws are formulated in terms of points, orthonormal tetrad frames, and components of the matter fields with respect to these frames. The laws are postulated to be gauge invariant under local Poincaré transformations. This implies the existence of 4 translational gauge potentials e α (“gravitons”) and 6 Lorentz gauge potentials Γαβ (“rotons”) and the coupling of the momentum current and the spin current of matter to these potentials, respectively. In this way one is led to a Riemann-Cartan spacetime carrying torsion and curvature, richer in structure than the spacetime of general relativity. The Riemann-Cartan spacetime is controlled by the two general gauge field equations (3.44) and (3.45), in which material momentum and spin act as sources. The general framework of the theory is summarized in a table in Section 3.6. - Options for picking a gauge field lagrangian are discussed (teleparallelism, ECSK). We propose a lagrangian quadratic in torsion and curvature governing the propagation of gravitons and rotons. A suppression of the rotons leads back to general relativity.

Given at the 6th Course of the International School of Cosmology and Gravitation on “Spin, Torsion, Rotation, and Supergravity, ’held at Erice, Italy, May 1979.

Supported in part by DOE contract DE-AS05-76ER-3992 and by NSF grant PHY-7826592.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, W. Germany

    Friedrich W. Hehl

  2. Center for Particle Theory and Center for Theoretical Physics, The University of Texas at Austin, Austin, Texas, 78712, USA

    Friedrich W. Hehl

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  1. Friedrich W. Hehl
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Editors and Affiliations

  1. Syracuse University, Syracuse, New York, USA

    Peter G. Bergmann

  2. University of Bologna, Bologna, Italy

    Venzo De Sabbata

  3. University of Ferrara, Ferrara, Italy

    Venzo De Sabbata

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© 1980 Plenum Press, New York

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Hehl, F.W. (1980). Four Lectures on Poincaré Gauge Field Theory. In: Bergmann, P.G., De Sabbata, V. (eds) Cosmology and Gravitation. NATO Advanced Study Institutes Series, vol 58. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3123-0_2

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  • DOI: https://doi.org/10.1007/978-1-4613-3123-0_2

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