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My background covers two years of QM, and I am now starting into QFT using Zee and Srednicki.

I am familiar with the math behind wave packets and their rapid dispersion, as one of the reasons they cannot represent particles. I have also covered QFT up to basic Feynman diagrams and the Dirac equation and the basic treatment of the fields as creation and annihilation operators.

My question is:

Can anybody describe, preferably in schematic terms if that's allowed here, (as I can study on this myself), how a particle appears from the underlying field.

I am fully aware that a complete description is not appropriate here.

To put it another way, I am looking for a roadmap of the steps involved in taking a field, for example the electron field, and getting a particle out of it.

I have searched for simple explanations and have come across the following:

Excitations in the field

The second answer in the post includes:

For the case of an electron, it is described by a Dirac spinor field $ψ$ with Lagrangian,

$$L=ψ¯(iγμ∂μ−m)ψ$$

We say the electron arises as an excitation of the quantum field $ψ$. On a technical level, if we expand the field using Fourier analysis, roughly like,

$$\psi \sim \int \frac{d^4p}{(2\pi)^4} \, \left( b_pe^{ipx}+c^\dagger_p e^{-ipx}\right)$$

neglecting many factors.

I can follow the structure of this equation, but if this is the basic "wave", what constraints must it obey to create an electron?

Again schematically only, if a quantum version of S.H.M is involved, I would like to know more. I think I read that a particle is connected with the smallest node, but I don't know if that makes sense to anyone.

  • Neither of those books will be able to explain you what you want to know. Rather, you will have to read Weinberg's books. Good luck! – AccidentalFourierTransform Jan 30 '18 at 19:56
  • @AccidentalFourierTransform Thank you, (I think :) At least that explains why I couldn't find anything in them despite skipping ahead. –  Jan 30 '18 at 19:58
  • I don't think you can get out an electron out of a field or it makes sense. First of all, all the fields are operators act on some state. and you can create or anhiliate a particle from that state, by simply applying those operators on that state. electron field is an operator that adds an electron to your state when applied to it. – physshyp Jan 30 '18 at 20:22
  • @physshypp thank you for your comment, I will read up on the relationship between fields and states. –  Jan 31 '18 at 09:10

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