[petschge]

In 2d electromagnetism splits light waves into TE and TM modes that don't couple to each others (until you add a dielectric). That is unusual to our 3d picture, but doesn't break electromagnetics.

And the generalization of the cross product, the wedge product works just fine in 2d. If you take the wedge of two 1-forms (vectors) in 2d you get a 2-form. In 3d that is equivalent to a (3-2)-form or in other words a (pseudo-)vector. In 2d you get a (2-2)-form or in other words a pseudo-scalar 0-form. That is of course nothing but the z component of the resulting pseudo-vector if you had done it in 3d. So EM in 2d might get flat landers started on weird group theory a bit early, but it is not fundamentally incompatible with life.