# Photon creation and quantum field theory

I remember learning the following familiar story in high school chemistry class:

"an atom consists of a nucleus of protons and neutrons, and a collection of electrons orbiting around the nucleus at discrete levels. When an electron drops from level n to level n-1, a photon is created."

I have subsequently learnt some more advanced physics, and I am now learning basic quantum field theory.

My question: how would one amend the story I learned in high school, given knowledge of basic quantum field theory?

The reason I am asking this question is because my quantum field theory textbook is teaching me how to calculate scattering cross sections, decay rates, ect. However, it's not at all clear to me what this has to do with the claim that a photon gets emitted when an electron drops one level.

• Are you looking for something like, "the matrix element of the EM creation operator between <Excited> and <Ground> is non-zero"? (I'm hoping someone better versed in QED than I can give the correct sentence...) – johndecker Aug 16 '18 at 8:23
• Have a look at physics.stackexchange.com/q/217239 – Henrikas Aug 16 '18 at 8:27
• @johndecker Yes, indeed. Ideally I would like either an explanation or a reference which explains how to convert my high-school physics story into QFT. – user142700 Aug 16 '18 at 8:40
• @Henrikas Thank you for the link! To clarify, I understand how one can explain the discreteness of orbitals using ordinary QM. However, I would also like to understand why photons are created when electrons change orbitals. – user142700 Aug 16 '18 at 8:41

The story of Quantum Field Theory(QFT) treats particles such as electron,proton or photon very differently from quantum mechanics(QM) and classical mechanics(CM).

We all know with CM we can't explain the behavior of an atom because according to Maxwell's theory accelerating particles should radiate their energy and for an atom this means that electrons should fall into nucleus by radiating energy.

QM says that electrons have defined stationary orbits and manages to explain phenomenon like black-body radiation. But QM also fails when particles have speed comparable to speed of light.

Now QFT is born which is a marriage of QM and Special Theory of Relativity. QFT treats particles as excited states of a field and interaction between particles is studied by interaction between fields. Standard Model is a result of QFT. If we want to study interaction between two electrons, we say that one electron applies force on other by virtue of photons. QFT also says that in vacuum a photon can create a electron-positron pair and electron-positron pair can annihilate to produce a photon. Of course the principal of conservation of energy and principal of conservation of momentum should be respected in any kind of process.

To explain the phenomenon of photon emission or photon absorption when electrons changes their orbits, the picture of QM works pretty well because electrons never reach speed of light unless they are put in an accelerator. Explaining the phenomenon by QFT, we can describe electron by an excited state of field 1(Dirac Field) and similarly photon by excited state of field 2(Maxwell Field). Now if photon is absorbed then the field 2 comes to it's ground states and field 1 moves to upper excited state. The mathematics of this process is not very easy and moreover it is very lengthy. If you want to see the mathematics I will strongly recommend chapter 8 for Dirac Field, chapter 9 for Maxwell Field from book Ashok Das-Lectures on QFT. For interaction of these two fields you can refer to chapter 5 from book Peskin,Schroeder- Introduction to QFT.