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The electromagnetic field tensor transforms according to the standard
rule

(1511) 
This easily yields the celebrated rules for transforming electromagnetic
fields:



(1512) 



(1513) 



(1514) 



(1515) 
where is the relative velocity between the primed and unprimed
frames, and the perpendicular and parallel directions are, respectively,
perpendicular and parallel to .
At this stage, we may conveniently note two important invariants of the
electromagnetic field. They are

(1516) 
and

(1517) 
The first of these quantities is a properscalar, and the second
a pseudoscalar.
Next: Potential due to a
Up: Relativity and electromagnetism
Previous: The dual electromagnetic field
Richard Fitzpatrick
20060202