Analytic definition of spin structure

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.

Updated bibliography

References in corpus (1)

• Spectral asymptotics for first order systems

Cited by in corpus (3)

• Diagonalization of elliptic systems via pseudodifferential projections
• Global propagator for the massless Dirac operator and spectral asymptotics
• Classification of first order sesquilinear forms