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Gravity in hyperspin manifolds

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Abstract

We seek the dynamics of a Bergmann manifold: a manifold of dimensionn=N 2 supporting a bundle of spinor spaces of dimensionN, and a mapσ from the tangent spaces to the Hermitian spinor forms. Even though the spin-vectorσ is the fundamental variable of the theory, every invariant analytic function depending onσ and its firstm derivatives alone can be expressed in terms of the chronometric tensorg and its firstm derivatives. Bergmann manifolds of dimensionn > 4 do not have invariant second-order equations forσ. We find a family of invariant actions which lead tonth-order quasilinear equations of motion on Bergmann manifolds and reduce to the Einstein-Hilbert action forn=2. The resulting gauge particles have spin, 1/2,1, 3/2, and 2.

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Authors and Affiliations

  1. Georgia Institute of Technology, 30332, Atlanta, Georgia

    Shlomit Ritz Finkelstein

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  1. Shlomit Ritz Finkelstein
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Finkelstein, S.R. Gravity in hyperspin manifolds. Int J Theor Phys 27, 251–272 (1988). https://doi.org/10.1007/BF00670753

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  • DOI: https://doi.org/10.1007/BF00670753

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