Feynman Diagrams- Not Conserving Momentum?

[nhmllr]

I'm reading QED. At first I thought I understood Feynman diagrams, but due to ones like these I'm not so sure anymore. In either of these diagrams, the photon "curves" around in space time. Why would it travel in anything BUT a straight line if nothing is influencing it? I liked to picture these diagrams in my head as billiard balls going around knocking into other ones, keeping momentum conserved. But here, momentum is CLEARLY NOT conserved. If you look at the initial state of (a) even, the electron is traveling slower at first, then speeds up! What's going on here!?

 

[haushofer]

Don't picture particles as billiard balls. Feynman diagrams are just convenient pictures to depict calculations. In QM, particles are also waves, so the whole notion of "particles as billiard balls" doesn't make sense at all. Also, you can't get any notion of speed from these diagrams.

Momentum is conserved at every vertex in these diagrams. It is given by the wavenumber of the particles.

 

[nhmllr]

Don't picture particles as billiard balls. Feynman diagrams are just convenient pictures to depict calculations. In QM, particles are also waves, so the whole notion of "particles as billiard balls" doesn't make sense at all. Also, you can't get any notion of speed from these diagrams.

Momentum is conserved at every vertex in these diagrams. It is given by the wavenumber of the particles.

Wait if the y-axis is time and the x is space, then a line with a greater slope is moving slower- right? Can't you tell speed like that- or am I reading too much into this?

 

[Bill_K]

You're reading too much into this. The only thing meaningful about the diagram is its topology.

 

[Dickfore]

Feynman diagrams are topological graphs. It only matters what points (vertices) are connected by the lines (propagators) and not their shape. When written in momentum space, there isn't even a time direction.

 

[nhmllr]

Feynman diagrams are topological graphs. It only matters what points (vertices) are connected by the lines (propagators) and not their shape. When written in momentum space, there isn't even a time direction.

But COULD you make a Feynman diagram with units? And if so, what would be happenig with these loopy photons?

 

[Dickfore]

But COULD you make a Feynman diagram with units? And if so, what would be happenig with these loopy photons?

What 'units'?

 

[haushofer]

But COULD you make a Feynman diagram with units? And if so, what would be happenig with these loopy photons?

No. That would imply that you know the exact trajectory of the electron as a point particle. Particles are waves in QM.

These loopy photons are a remnant of the fact that you're doing perturbation theory, and are called "virtual". They never appear in an in- or outstate, as such are never directly measured, and as such cannot be assigned a velocity or definite energy.