# Signicance of positive and negative frequencies?

1. Sep 11, 2010

### pellman

Reading some QFT in which we are faced with inhomogeneous equation

$$(\partial^\mu \partial_\mu + m^2)\phi(x)=J(x)$$

The solution is given as

$$\phi(x)=\phi^{(+)}_{in}(x)+\phi^{(-)}_{out}(x)+i\int{d^4 x\Delta(x-x')J(x')$$

where $$\Delta$$ is the appropriate Green's function. "in" means the solution for early times (when J vanishes) and "out" for late times (when J vanishes). The text states "where the superscripts (+) and (-) indicate the positive- and negative-frequency parts, respectively."

I don't understand why the in- and out-solutions are restricted to the positive- and negative-frequency parts.

2. Oct 25, 2010

### pellman

bump. I'm still interested in this. Maybe someone is around now who can look at it.

Just one little bump. Any insight is appreciated.

3. Oct 25, 2010

### Avodyne

The formula is inconsistent with the text. phi plus can't be the solution at early times, because the formula also inlcudes phi minus.

My recommendation: find a better QFT text.

4. Oct 25, 2010

Ok. Thanks.