I have a question about probabillity of photon from electromagnetic fields.
We know that electromagnetic four-potential, which can be found with QED equations
$A_{\mu}=\bigl(\begin{smallmatrix}\frac{\phi}{c} & A_x & A_y & A_z\end{smallmatrix}\bigr)$
Such that
$ \vec{E}=-\nabla\: \phi-\frac{\partial \vec{A}}{\partial t}$
$ \vec{B}=\nabla × \:\vec{A}$
How do I get photon probabillity out of this potential?
Best Answer
In quantum field theory, observables (such as decay rates and scattering cross sections) are probabilistic and often characterized in terms of correlation functions. For example:
where $|0\rangle$ is the vacuum state.
There are important subtleties related to operator ordering, Lorentz transformations, and gauge invariance that I am suppressing in this answer for simplicity; if you want the full story you will need to work through a quantum field theory text. David Tong's lecture notes are a good resource https://www.damtp.cam.ac.uk/user/tong/qft.html.
The correlation functions are computed using the Hamiltonian of the system, typically using the Dyson series.