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$$\mathcal{L}=\partial_{\mu}\chi^{*}\partial^{\mu}\chi-m_{\chi}^{2}\chi^{*}\chi.$$

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}##?