= Fermionic current on the circle
{title2=$J_n=\sum_r:c_r^*c_{r+n}:$}
= Fermionic currents on the circle
{synonym}
A Fourier mode of the normal-ordered fermion density is a fermionic current. On the finite-energy domain its defining sum has finitely many nonzero actions on each occupation vector. The modes satisfy $J_n^*=J_{-n}$ and $[J_n,J_m]=n\delta_{n+m,0}I$. The zero mode is charge; positive modes annihilate charge ground states and negative modes create the oscillators in the <fermion-boson correspondence on the circle>.
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