Normalization of a complex scalar propagator (source code)

= Normalization of a complex scalar propagator
{title2=$C=\zeta^{-1}D_F$}

For positive kinetic coefficient $\zeta$ in $\mathcal L_0=\zeta(\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi)$, the <canonical momentum> is $\pi_\phi=\zeta\dot\phi^*$. Positive-energy oscillator modes with unit oscillator <commutators> have amplitude $1/\sqrt{2\zeta E_{\mathbf p}}$. The mixed time-ordered <propagator> is $C=\zeta^{-1}D_F$, with $D_F$ the ordinary <scalar propagator>. This also follows by inverting the quadratic form in the <path integral>. Rescaling $\phi$ changes interaction coefficients as well as external correlation-function factors.