# The Effective Lagrangian of the Electromagnetic Field

1. Oct 5, 2014

### r.sahebi

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. Oct 5, 2014

### dextercioby

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).

3. Oct 6, 2014

### r.sahebi

yes, thats my wrong
can you tell me how i can have it?

4. Oct 6, 2014

### vanhees71

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).

5. Oct 6, 2014

### r.sahebi

thanks a lot.