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I try to understand Cherenkov radiation from a quantal point of view. I searched for research papers on this topic, but I am not satisfied with what I found so far. So maybe you can help me.

What I want to calculate is the matrix element for emission of a Cherenkov photon by a moving electron. The Feynman diagram for this process is described by an incoming electron and an outgoing electron + photon (no internal lines anywhere). This first order process would be forbidden in vacuum but is allowed in solids. To calculate now the matrix element for this process, what should I use for the electromagnetic vector potential that describes the photon? As I see it, it should just be like in the free case but with a modified relation between the energy and wave vector of the photon due to the permittivity of the medium. What do you think?

Greetings, Syrius

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# Quantized Cherenkov Radiation

Can you offer guidance or do you also need help?

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