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The Effective Lagrangian of the Electromagnetic Field

  1. Oct 5, 2014 #1
    hi to everyone

    as you know it is the lagrangian equation
    the effective Lagrangian of the electromagnetic field is given by following relation in gaussian units.
    L=(1/8pi) (E^2-B^2)
    how is must calculate this relation?

    (the energy density of electromagnetic fields is given by u=(1/8pi) (E^2+B^2) )
  2. jcsd
  3. Oct 5, 2014 #2


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    I don't know why you'd call that 'effective', that is the normal lagrangian density of the e-m field (without gauge fixing, of course).
  4. Oct 6, 2014 #3
    yes, thats my wrong
    can you tell me how i can have it?
  5. Oct 6, 2014 #4


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    This comes out from a careful analysis of the unitary representations of the Poincare group. This Lagrangian is the only one for a free massless vector field (written in its representation as a four-vector field) with only discrete intrinsic (helicity) degrees of freedom and admitting space-inversion symmetry (parity invariance). This can only be realized in terms of an Abelian gauge theory. For details, see


    (Appendix B).
  6. Oct 6, 2014 #5
    thanks a lot.
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