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Results tagged with curvature
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user 130740
Use this for questions pertaining to curvature of manifolds. Does not need to be specific to general relativity, but also for curvature of e.g. a Calabi-Yau manifold.
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Derivation of expression for Berry curvature
\end{align*}
The Berry curvature is obtained by taking the exterior derivative of $\mathcal{A}$,
\begin{align*}
\mathcal{F}&=d\mathcal{A}=\frac{d\bar{v}(k)\wedge dv(k)}{(1+|v(k)|^2)}-\frac{|v(k)|^2d\bar … The expression found for the curvature also shows, explicitly, that the first Chern number is the degree/winding number of the map $\Phi:k\mapsto \vec{x}(k)= \vec{h}(k)/|\vec{h}(k)|\in S^2$,
\begin{align …