Complex scalar field - Feynman integral

[ryanwilk]

Homework Statement

For a real scalar field $\phi$, the propagator is $\frac{i}{(k^2-m_\phi^2)}$.

If we instead assume a complex scalar field, $\phi = \frac{1}{\sqrt{2}} (\phi_1 + i \phi_2)$, where $\phi_1,\phi_2$ are real fields with masses $m_{\phi 1},m_{\phi 2}$, what is the propagator?

Homework Equations

N/A

The Attempt at a Solution

Is this true?: There's a 1/2 probability that the propagator has mass $\phi_1$, $\phi_2$ so the propagator should just be $\frac{1}{2} [ \frac{i}{(k^2-m_{\phi_1}^2)} + \frac{i}{(k^2-m_{\phi_2}^2)} ]$. But how does the 'i' change things?

Any help would be appreciated,

Thanks.

 

[dextercioby]

The Euler-Lagrange eqns (which typically determine the Feynman propagator) are completeley separated and identical with the original KG equation. So indeed the propagator will be written as a sum b/w a term with i and the other with i².