- #1

EuphoGuy

- 8

- 0

[tex] \mathcal{L} = B_i B_i + A_i ( h^*\partial_i h - \partial_i h^* h ) + A_i A_i h^* h [/tex]

(this isn't gauge invariant because I haven't included the other relevant terms, but these are the only ones that contribute to the EOM)

If I impose the coulomb gauge \partial_i A_i = 0, the gauge fixed lagrangian is

[tex] \mathcal{L} = - A_i \nabla^2 A_i + A_i h^* \partial_i h + A_i A_i h^* h [/tex]

giving equation of motion

[tex] \nabla^2 A_i = h^* \partial_i h + 2 A_i h^* h [/tex]

If I took the divergence of this I would get 0 on the left but not on the right. Is this something one has to worry about then? Fixing gauges that are inconsistent with equations of motion? I think I'm rather just making a silly mistake, since given any old A, there's no reason I can't take it to coulomb gauge.

Thanks for the help!