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.
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Research Article| August 02 2017
Analytic definition of spin structure
Zhirayr Avetisyan ;
Nikolai Saveliev ;
Zhirayr Avetisyan, Yan-Long Fang, Nikolai Saveliev, Dmitri Vassiliev; Analytic definition of spin structure. J. Math. Phys. 1 August 2017; 58 (8): 082301. https://doi.org/10.1063/1.4995952
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