# Green's Functions and Feynman Diagrams

1. May 28, 2015

### rolotomassi

I've been learning about Greens functions. I'm familiar with how to find them for different differential operators and situations but far from fully understanding them. We were shown in lecture how they can be used to obtain a perturbation series, leading to Feynman diagrams which represent them. But there was no mention about virtual particles which is what I thought closely related to Feynman diagrams. You include all of the ways a particle and emit, re-absorb and do whatever with the virtual particles and the more events you include the more terms in the series and the more accurate etc..

Do virtual particles arise as a mathematical consequence of Greens function then, and if so how?

2. May 28, 2015

### DrDu

Yes, all of the lines in a diagram which correspond to particles whose energy and momentum don't fulfill $E^2=m^2c^4+p^2c^2$ are virtual particles (one says also "off the mass shell").
This doesn't mean that virtual particles really exist, rather, they are a consequence of the perturbation series one is using.

3. May 28, 2015

### The_Duck

In the perturbation series for quantum field theory, each term can be represented by a Feynman diagram. These diagrams consist of external legs, internal legs, and vertices. The external legs represent initial- and final-state particles. The internal legs stand for Green's functions of the differential operators corresponding to the equations of motion of particles. These Green's functions can be thought of as giving the amplitude for a particle to propagate from one place to another. So we call the internal legs "virtual particles" and we think of the vertices as representing the emission or absorption of particles.

4. May 28, 2015

### rolotomassi

Thanks a lot. Big help