Photon and anti-photon annihilation?

[Goliatbagge]

Photon and "anti-photon" annihilation?

In quantum field theory pairs of virtual particles can appear from vacuum and quickly annihilate each other, for example an electron/positron or a proton/antiproton. But how does this work with photons?From what I know, the photon is its own anti-particle. So the "anti-photon" is just another photon. But how can a real photon annihilate an other "real" photon? Real photons are everywhere, so in that case photons would annihilate each other all the time?

 

[sadraj]

The difference between photon and other massive particles is that the Number Operator of photons is not conserved. What is conserved is the sum of energy of the photons not their number.

 

[Goliatbagge]

So if two photons appear from vacuum their sum of energy should be zero? Wouldn't that mean that one of them must have negative energy?

 

[vanhees71]

In principle, photons can annihilate, e.g., through the QED process $\gamma+\gamma \rightarrow e^+ + e^-$. I've never heard that anyone has been able to observe this process, however.

 

[Hawkwind]

I think that this process has in fact been observed - even for real photons:

Positron production in multiphoton light-by-light scattering

... followed by
a collision between the high-energy photon and several laser photons to produce
an electron-positron pair. These results are the rst laboratory evidence for
inelastic light-by-light scattering involving only real photons.

 

[Drakkith]

So if two photons appear from vacuum their sum of energy should be zero? Wouldn't that mean that one of them must have negative energy?

I don't believe so. Consider the creation of an electron and a positron. The total mass-energy would be positive, but because they only exist for an instant before annihilation, no conservation rules are violated.

Also, note that "real" photons are not created directly from the vacuum, but from accelerated charges.

 

[Bill_K]

Consider the creation of an electron and a positron. The total mass-energy would be positive, but because they only exist for an instant before annihilation, no conservation rules are violated.

Since energy is conserved, the total mass-energy will be zero, just like the vacuum they emerged from. Virtual particles don't have to obey the usual relationship between energy and momentum, and it's perfectly OK for one particle or the other to have negative energy.

 

[vanhees71]

What do you mean by "total mass-energy"? Of course the two real photons are onshell and the scattering process $\gamma + \gamma \rightarrow e^+ + e^-$ obeys energy-momentum conservation. You can analyze the kinematics as usual with help of the Mandelstam variables.

 

[Hawkwind]

The experiment is about a scattering process with REAL photons (originating from laser sources). Of course, these photons have positive energies (frequencies).