Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The Effective Lagrangian of the Electromagnetic Field

  1. Oct 5, 2014 #1
    hi to everyone

    L=T-V
    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

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    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

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    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

    http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

    (Appendix B).
     
  6. Oct 6, 2014 #5
    thanks a lot.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook