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I've tried working out the Heisenberg EOM for the 4-current operator. Two very beautiful articles (DOI: 10.1103/PhysRevA.84.042107, DOI: 10.1103/PhysRevA.90.012508) present this result, but I have not managed to follow through with the (largely absent) calculation. My crux lies also with the left-pointing-vector on top of one of the nablas (attached image). And they don't define it anywhere in the papers! Could someone help me make sense of it?

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$\stackrel{\leftarrow}{\nabla}$ means that the differential operator $\nabla$ differentiates to the left, i.e. it differentiates the fermion spinor $\hat{\bar{\psi}}$ in eq. (43).

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  • $\begingroup$ Many thanks! Now it all works out :) $\endgroup$
    – Sphyr
    Commented Aug 11 at 17:43

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