Analytic definition of spin structure

Zhirayr Avetisyan, Yan Long Fang, Nikolai Saveliev, Dmitri Vassiliev

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number082301
JournalJournal of Mathematical Physics
Issue number8
StatePublished - Aug 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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