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A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry

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Abstract

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics.

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Authors and Affiliations

  1. Dipartimento di Scienze Fisiche, Università di Napoli “Federico II”, Napoly, Italy

    S. Capozziello & M. De Laurentis

  2. INFN Sez. di Napoli, Compl. Univ. Monte S. Angelo, Ed. N, Via Cinthia, 80126, Napoli, Italy

    S. Capozziello & M. De Laurentis

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  1. S. Capozziello
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  2. M. De Laurentis
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Correspondence to S. Capozziello.

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Capozziello, S., De Laurentis, M. A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry. Found Phys 40, 867–899 (2010). https://doi.org/10.1007/s10701-009-9367-9

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  • DOI: https://doi.org/10.1007/s10701-009-9367-9

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