We present a three-dimensional metric affine theory of gravity whose field equations lead to a connection introduced by Schrodinger many decades ago. Although involving nonmetricity, the Schrodinger connection preserves the length of vectors under parallel transport, and appears thus to be more physical than the one proposed by Weyl. By considering solutions with constant scalar curvature, we obtain a self-duality relation for the nonmetricity vector which implies a Proca equation that may also be interpreted in terms of inhomogeneous Maxwell equations emerging from affine geometry. (C) 2021 The Authors. Published by Elsevier B.V.
Schrödinger connection with selfdual nonmetricity vector in 2+1 dimensions / S. Klemm, L. Ravera. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - 817:(2020 Aug 28), pp. 136291.1-136291.4. [10.1016/j.physletb.2021.136291]
Schrödinger connection with selfdual nonmetricity vector in 2+1 dimensions
S. KlemmPrimo
;
2020
Abstract
We present a three-dimensional metric affine theory of gravity whose field equations lead to a connection introduced by Schrodinger many decades ago. Although involving nonmetricity, the Schrodinger connection preserves the length of vectors under parallel transport, and appears thus to be more physical than the one proposed by Weyl. By considering solutions with constant scalar curvature, we obtain a self-duality relation for the nonmetricity vector which implies a Proca equation that may also be interpreted in terms of inhomogeneous Maxwell equations emerging from affine geometry. (C) 2021 The Authors. Published by Elsevier B.V.File | Dimensione | Formato | |
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