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I have a conceptual difficulty in understanding the electron spin. On the one hand, it is an experimental, observable feature of electrons. The problem is in understanding to what it belongs - to a bare electron or to an electron already coupled to the electromagnetic field. I think it is the latter. In other words, the electron spin characterizes a complicated object (a real system) rather than a "free" (non interacting) electron. It is like the total spin of a compound system. On the other hand, in theory we ascribe it to a "bare" electron solely. Do you think we have a conceptual problem here?

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closed as not constructive by mbq Apr 29 '11 at 19:57

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Yes, there could be a conceptual problem. But as far as I know there is no other behaviour known from any experiment so it might indeed be that we can assume the electron to be described in the sense we know. –  Robert Filter Apr 29 '11 at 16:59

1 Answer 1

There is no conceptual problem. The bare electron field is a Dirac, spin-1/2 field, and so is the renormalized field. A bare electron carries $j=1/2$, and so does the physical, renormalized electron.

In fact, because spin is a discrete quantum number, a continuous process such as renormalization (a process that depends either on a continuous coupling $e$ or the mass scale $\mu$) couldn't change the value of such a quantum number.

So the equal value of both spins is not only free of contradictions; it is inevitable.

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Hi Lubosh, I am glad that you admit that the spin 1/2 belongs to the real, renormalized, dressed electron. This is what I would like to underline: it is a spin of a compound system. It is not so evident. You know, an atom, as a compound system, may have the the angular momentum 1/2 but it is not obligatory. A compound system may have different total angular momenta. Besides, your argument about discreteness of quantum number is not convincing. First, there is no explicit solution for a renormalized electron to judge. Next, renormalizations change nothing by definition, not only spin. –  Vladimir Kalitvianski Apr 29 '11 at 18:10

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