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Analytic definition of spin structure

Avetisyan, Z; Fang, Y-L; Saveliev, N; Vassiliev, D; (2017) Analytic definition of spin structure. Journal of Mathematical Physics , 58 , Article 082301. 10.1063/1.4995952. Green open access

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Abstract

We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion. Our analytic definition relies on the use of the concept of a non-degenerate two-by-two formally self-adjoint first order linear differential operator and gauge transformations of such operators. We also give an analytic definition of spin structure for the 3-dimensional Riemannian case.

Type: Article
Title: Analytic definition of spin structure
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/1.4995952
Publisher version: http://dx.doi.org/10.1063/1.4995952
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.
Keywords: Riemannian manifolds, Algebraic topology, Operator theory, Gauge field theory, Theory of relativity
UCL classification: UCL
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/1531510
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