# How to create charge from light?

1. Feb 15, 2009

### per.sundqvist

We know that we can create an electron-positron pair out of a gamma-ray, if it has an energy of $$E=h\nu>2m_ec^2$$.

However a photon is described as an EM-wave that obeys the divergence criteria
$$\nabla\cdot\vec{E}=0$$

My question is simply if there is a "simple" explanation out there (QFT?) which describes microscopically what happens when the photon breaks up and 2 charged packages are created? I also wonder what the distance between the particles is in the creation moment.

My guess is that the EM-wave/photon must be disturbed in some way (by gravity?) such that it bends in some way, and that it is this bending which gives rise to the charge creation: $$\nabla\cdot\vec{E}=\rho/\epsilon$$, but where the total charge is neutral, like in the point-particle classical situation:
$$\rho=e(\delta(r-a)-\delta(r+a))$$ (some kind of dipole, but perhaps rater described with waves)

Any idea?

2. Feb 15, 2009

### clem

Pair production requires an external force, which is usually the Coulomb force of a nucleus.
QED gives a relatively simple explanation.

3. Feb 15, 2009

### per.sundqvist

Ok thanks! I'm a little confused still since the four-potential $$A_{\mu}$$ in the QED-Lagrangian is the self-field. Do you use superposition in the case of a Coulomb potential, like $$A_{\mu}=A_{0,ext}(Coulomb)+A_{\mu}(self)$$?

4. Feb 15, 2009

### confinement

Maybe it is just a personal shortcoming, but I am not aware of any QFT description at the level of realistic detail that you are describing.

Just as a particle in QM travels on all possible paths, so does a field in QFT take on all possible configurations. If we treat both the electrons and the vector potential as quantum field excitations (respectively, as a dirac field and a gauge field) then we are to think of the electron-positron pair creation/annihilations as happening super-frequently all over space. But there are no exact solutions to QFT, only perturbative expansions, meaning that we usually only take into account the simplest, and in QED most dominant, modes of creation/anihilation, when calculating the amplitude for some process.

Perhaps with an exact solution to QED it would be possible to give a more meaningful anwer, but at our current level of description these details are unknown to us.