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How to deal with $\vec{j}\cdot\vec{A}$ or $\rho A^2$ interaction when utilizing Kubo formula? Gauge invariance?

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If there exist electromagnetic fields in solids, electrons can feel interactions like $\vec{j} \cdot \vec{A}$ or $\rho A^2$ (these are not regarded as perturbations). But these are not gauge invariant. Then we add some other perturbation fields to study their corresponding linear response. I can't see whether brute-force Kubo formula evaluation gives gauge invariant result.

This post imported from StackExchange Physics at 2014-08-22 05:09 (UCT), posted by SE-user huotuichang

asked Mar 16, 2014 in Theoretical Physics by sfman (270 points) [ no revision ]

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