Is the generalized ohm's law on the model page correct?

[cuphyalex]

The Ohm's law model page (https://warpx.readthedocs.io/en/latest/theory/models_algorithms/kinetic_fluid_hybrid_model.html) shows this:
$en_e\vec{E} = \frac{m}{e}\frac{\partial \vec{J}_e}{\partial t} + \frac{m}{e}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e$

, while the ones I found in many places have no negative sign before the j cross B term.

In my simulation result, I also found the E = j_displacement cross B ($en_e\vec{E}=\vec{j_e}\times\vec{B}$) without a negative sign.