Factors in the theory of a complex scalar field

[spaghetti3451]

The theory of a complex scalar field $\chi$ is given by

$$\mathcal{L}=\partial_{\mu}\chi^{*}\partial^{\mu}\chi-m_{\chi}^{2}\chi^{*}\chi.$$
Why is it not common to include a factor of $\frac{1}{2}$ in front of the complex $\chi$ kinetic term?

What is the effect on the propagator of including a factor of $\frac{1}{2}$?

 

[dextercioby]

A rescaling of the mass term. Think about the real field and about the 1/2 mv^2 for Galilean particles.