R-\xi gauge with complex generators

Hi, I would like to know how to used R-\xi gauge for complex
generators. I looked in Weinberg and Peskin but they replace the
complex fields \phi_i i=1,\cdots,N by a real field \phi_i,
i=1,\cdots,2N. Keeping complex fields instead, the calculation can be
done easily but the gauge-fixing term will be complex (of the form
f_\alpha^\dagger f_\alpha following Weinberg). From there, to find the
ghost Lagrangian, we must use complex ghost fields. It seems strange
to me because I've never seen that before. Does it really imply that
the ghost are complex ?

.

Quantcast