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Invariant quantities in the EM field

  1. Jan 23, 2007 #1


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    I understand that the quantities

    [tex]E^2 - B^2[/tex]

    [tex]\vec{E} \cdot \vec{B}[/tex]

    (the dot is vector inner product).
    where E and B are the electric and magnetic components of an EM wave,
    are invariant under Lorentz/Poincare transformations.
    Can someone explain the physical significance of this ? Is either quantity related to the velocity of light ( or the invariance of the velocity of light ) ?

    The second expression must be zero at all times surely ?
    Last edited: Jan 23, 2007
  2. jcsd
  3. Jan 24, 2007 #2


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    Not necessarily wave. An EM wave is just a particular case of a radiated EM field. That's why the scalar product is not always 0, because the radiated EM field is not always a wave.

    There's not too much physical significance of the invariants, just that the first one is good for a lagrangian density since it leads to field equations second order in time.

  4. Jan 24, 2007 #3


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    Thanks, Daniel.

    I didn't know there are solutions to Maxwells equations other than the EM wave.

    It's hard getting my head around the idea that the E and B fields 'mix' like space and time, when boosted.
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