Feynman diagram for pair annihilation

[spaghetti3451]

Hi,

I've been reading about Feynman diagrams lately and I'm trying to understand the pair annihilation diagram. The picture's here: http://en.wikipedia.org/wiki/File:Feynman_EP_Annihilation.svg

I don't understand the following things about the diagram:

1. Why anti-patricles have to travel backward in time
2. What the horizontal solid line represents
3. Why gamma rays come out of both vertices.

Any help would be greatly appreciated.

 

[Bill_K]

1. Why anti-patricles have to travel backward in time

They don't. Antiparticles always travel forward in time, just like particles. The arrow on the line doesn't indicate it's traveling backwards in time, it just symbolizes the fact that this is an antiparticle.

2. What the horizontal solid line represents

An internal line in a Feynman diagram represents a virtual particle or propagator, in this case an electron propagator. A virtual particle shares most of the properties of a real particle except for the relationship between rest mass, energy and momentum.

3. Why gamma rays come out of both vertices.

A vertex in a Feynman diagram indicates an interaction, in this case an electron emitting a photon. You could draw a diagram with only one vertex and one photon emitted, but as the accompanying text in Wikipedia explains, annihilation into just one photon cannot take place because of energy-momentum conservation.

 

[bapowell]

1. Why anti-patricles have to travel backward in time

Particles traveling backwards in time are mathematically equivalent to antiparticles traveling forwards in time. Physically, however, we deal with antiparticles moving forwards in time.

 

[spaghetti3451]

Particles traveling backwards in time are mathematically equivalent to antiparticles traveling forwards in time. Physically, however, we deal with antiparticles moving forwards in time.

I see! So, just to be sure, we want to deal with only electrons, which is why electrons are made to travel backward in time to mean that positrons are moving forward in time?

 

[spaghetti3451]

An internal line in a Feynman diagram represents a virtual particle or propagator, in this case an electron propagator. A virtual particle shares most of the properties of a real particle except for the relationship between rest mass, energy and momentum.

Thanks for your help!

I'm trying to figure out why the internal line has to point in the direction of the positron's vertex. Is it because the virtual particle is emitted by an electron and absorbed by a positron?

 

[ChrisVer]

forward/backward in time is just an interpretation of the negative energy solutions of Relativistic quantum mechanics. In a very rough sense, instead of having negative energy, you have traveling backward in time. An electron traveling backwards in time is seen as a positron traveling forward in time.

There is no actual meaning in where the virtual particle points at... in physics, we integrate the propagator over all points in spacetime. Thus you can grab the 2 vertices, move them around and get the same image the other way( emission from positron and absorption by electron).