Add the Hermetian conjugate to make Lagrangian real

[Lapidus]

How does adding a h.c. term make a Lagrangian real? Like http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf on page 99 (11.51)?

thanks in advance

 

[mfb]

You add something with the same real part but with the negative imaginary part. The sum has an imaginary component of zero.

$z + \bar z$ is always real (even if you replace z by more complex structures).