A QHE: rotational invariance, no terms linear in E or B

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'Let’s first see what all of this means in the context of d = 3 + 1 dimensions. If we have rotational invariance then we can’t write down any terms linear in E or B. The first terms that we can write down are instead ...'

Why is this? I don't understnad . My thoughts would be pictruing the set up needing to be rotationally invariant, and since E and B are perpendicular a linear term alone wouldn't do this, but this wouldnt explaiin why E.E and B.B are invariant, I dont really know what I'm talking about, as you can tell

many thanks in advance


http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf , page 145 David Tong notes QHE , chapter 5 (eq. 5.5)
 
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Why is this?
Because vectors are not invariant under rotations: the rotation makes them point in a different direction. But the magnitudes of vectors are invariant under rotations, since rotation doesn't change the length of a vector, only its direction.
 

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