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Classification of first order sesquilinear forms

Capoferri, M; Saveliev, N; Vassiliev, D; (2020) Classification of first order sesquilinear forms. Reviews in Mathematical Physics , 32 , Article 2050027. 10.1142/S0129055X20500270. Green open access

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Abstract

A natural way to obtain a system of partial differential equations on a manifold is to vary a suitably defined sesquilinear form. The sesquilinear forms we study are Hermitian forms acting on sections of the trivial n-bundle over a smooth m-dimensional manifold without boundary. More specifically, we are concerned with first order sesquilinear forms, namely, those generating first order systems. Our goal is to classify such forms up to GL(n,) gauge equivalence. We achieve this classification in the special case of m = 4 and n = 2 by means of geometric and topological invariants (e.g., Lorentzian metric, spin/spinc structure, electromagnetic covector potential) naturally contained within the sesquilinear form - a purely analytic object. Essential to our approach is the interplay of techniques from analysis, geometry, and topology.

Type: Article
Title: Classification of first order sesquilinear forms
Open access status: An open access version is available from UCL Discovery
DOI: 10.1142/S0129055X20500270
Publisher version: https://doi.org/10.1142/S0129055X20500270
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Sesquilinear formsfirst order systemsgauge transformationsspinc structure
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/10092425
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