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Spacetime diffeomorphisms as matter fields

Capoferri, M; Vassiliev, D; (2020) Spacetime diffeomorphisms as matter fields. Journal of Mathematical Physics , 61 (11) , Article 111508. 10.1063/1.5140425.

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Abstract

We work on a 4-manifold equipped with Lorentzian metric g and consider a volume-preserving diffeomorphism that is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric h, the pullback of g. Motivated by elasticity theory, we introduce a Lagrangian expressed algebraically (without differentiations) via our pair of metrics. Analysis of the resulting nonlinear field equations produces three main results. First, we show that for Ricci-flat manifolds, our linearized field equations are Maxwell's equations in the Lorenz gauge with exact current. Second, for Minkowski space, we construct explicit massless solutions of our nonlinear field equations; these come in two distinct types, right-handed and left-handed. Third, for Minkowski space, we construct explicit massive solutions of our nonlinear field equations; these contain a positive parameter that has the geometric meaning of quantum mechanical mass and a real parameter that may be interpreted as electric charge. In constructing explicit solutions of nonlinear field equations, we resort to group-theoretic ideas: We identify special four-dimensional subgroups of the Poincaré group and seek diffeomorphisms compatible with their action in a suitable sense.

Type: Article
Title: Spacetime diffeomorphisms as matter fields
DOI: 10.1063/1.5140425
Publisher version: https://doi.org/10.1063/1.5140425
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10115933
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