TPM Lecture: On the Aharonov-Bohm effect for curved magnetic fields in 3-dimensions.

Who: Jan Philip Solovej (University of Copenhagen)
When: Monday, November 5, 2018 at 14:15
Where: The CP³ meeting room

I will review the celebrated Aharonov-Bohm effect and in particular discuss its generalization to curved solenoids in 3 dimensions. I will then discuss the effect for massless Dirac fermions where there is a natural spectral flow of the corresponding families of Dirac operators parametrized by the magnetic flux. I will define spectral flow and discuss how it can be computed explicitly in the Dirac-Aharonov-Bohm case for a large class of field line geometries given as knots or links. The spectral flow will, indeed, depend on the geometry and not only the topology of the links.