Parallel transporting a state along a geodesic doesn't introduce any anholonomy angle, that's what I learned in general relativity. In quantum mechanics, this anholonomy for states are related to the Berry phase. As one takes the state $$ \begin{pmatrix}\cos(\frac{\theta}{2}) \\ \sin(\frac{\theta}{2})e^{i \phi} \end{pmatrix} $$ And performs a parallel transport along the equator of the Bloch sphere (or along any other great circle for that matter) on obtains a $-\pi$ Berry phase. But I thought there was no anholonomy when you go along a geodesic, here along the great circles of the Bloch sphere.

The $-\pi$ Berry phase makes sense if we see it from the other viewpoint that an electronic wave function gets a $\exp(-i \pi)$ as it rotates $2\pi$. What I'm missing about the parallel transport in this case?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.