# Thread: anomalous magnetic moment of the electron

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## anomalous magnetic moment of the electron

I saw that there are correction factors for the anomalous magnetic moment of the electron. One of which is fine structure constant over 2pi. How are the others calculated?

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Originally Posted by Copernicus
I saw that there are correction factors for the anomalous magnetic moment of the electron. One of which is fine structure constant over 2pi. How are the others calculated?

I actually just want to know what the other correction for the g-factor for intrinsic electron magnetic moment. The first is fine structure constant over 2pi, but I can't find reference to the others.

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Originally Posted by grapes
It is here http://en.wikipedia.org/wiki/Anomalo..._dipole_moment

5. At the bottom of the wiki is a link to this abstract: http://arxiv.org/abs/hep-ph/9602417

Is that what you're looking for?

6. Okay, looking in my books (QED by Landau & Lif****z) I find the following comments: (and the board software does not like "Lifs" and "hitz" together)

Originally Posted by LL section 41
... including a particle which has an "anomalous" gyromagnetic ratio not describable by the Dirac equation.

The object is to derive an "equation of motion" for the spin when the particle moves in any (given) manner. Let us first take the non-relativistic case.

The non-relativistic Hamiltonina fo a particle n an external field is:

where H' includes all terms independent of the spin (see QM, paragraph 111) ...
Then we move on to section 118:

Originally Posted by LL section 41
As has been shown in 116, the value of g(0) determines the radiative correction to the magnetic moment of the electrons. [skip a bit and then find the correction in Eq. (118.2)]

a formula first derived by Schwinger (1949).
Then the section goes on deriving further corrections (terms in α2), of which apparently the derivation is rather complex and lengthy, LL only give the result for g2(0), which is:

The term at the RHD is the next term correction factor. You can get the whole derivation in C.M. Sommerfield (1957) and A. Peterman (1957). Note that this consists of several processes that are generating the g2(0).

I am not going to copy all of this, you can find a whole discussion of this topic in Landau & Lif****z Quantum Electrodynamics. Interestingly, I cannot find a literature section in the book, so you will have to go to ADS with the references above.

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Originally Posted by tusenfem
Okay, looking in my books (QED by Landau & Lif****z) I find the following comments: (and the board software does not like "Lifs" and "hitz" together)

Then we move on to section 118:

Then the section goes on deriving further corrections (terms in α2), of which apparently the derivation is rather complex and lengthy, LL only give the result for g2(0), which is:

The term at the RHD is the next term correction factor. You can get the whole derivation in C.M. Sommerfield (1957) and A. Peterman (1957). Note that this consists of several processes that are generating the g2(0).

I am not going to copy all of this, you can find a whole discussion of this topic in Landau & Lif****z Quantum Electrodynamics. Interestingly, I cannot find a literature section in the book, so you will have to go to ADS with the references above.
Wow! Thanks!

Is the term on the right supposed to be negative? What did you think of the derivation of the number? Is this for the intrinsic spin of the electron? I'll be checking out the book.

8. Originally Posted by Copernicus
Is the term on the right supposed to be negative?
The wiki page says that alpha/(2 pi), the first term of the correction, is 0.001164... but the current experimental value is only 0.00115965... so we need at least one negative term.

What's really nice is you can take tusenfem's TEX text and just copy it to wolframalpha.com and get -0.3284789...

\left(\frac{197}{144} + \frac{\pi^2}{12} - \frac{1}{2}\pi^2 \log(2) + \frac{3}{4}\zeta(3)\right)

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Originally Posted by tusenfem
Okay, looking in my books (QED by Landau & Lif****z) I find the following comments: (and the board software does not like "Lifs" and "hitz" together)

Then we move on to section 118:

Then the section goes on deriving further corrections (terms in α2), of which apparently the derivation is rather complex and lengthy, LL only give the result for g2(0), which is:

The term at the RHD is the next term correction factor. You can get the whole derivation in C.M. Sommerfield (1957) and A. Peterman (1957). Note that this consists of several processes that are generating the g2(0).

I am not going to copy all of this, you can find a whole discussion of this topic in Landau & Lif****z Quantum Electrodynamics. Interestingly, I cannot find a literature section in the book, so you will have to go to ADS with the references above.
How is the following term calculated out? I am not familiar with it?

Thanks

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Originally Posted by tusenfem
Okay, looking in my books (QED by Landau & Lif****z) I find the following comments: (and the board software does not like "Lifs" and "hitz" together)

Then we move on to section 118:

Then the section goes on deriving further corrections (terms in α2), of which apparently the derivation is rather complex and lengthy, LL only give the result for g2(0), which is:

The term at the RHD is the next term correction factor. You can get the whole derivation in C.M. Sommerfield (1957) and A. Peterman (1957). Note that this consists of several processes that are generating the g2(0).

I am not going to copy all of this, you can find a whole discussion of this topic in Landau & Lif****z Quantum Electrodynamics. Interestingly, I cannot find a literature section in the book, so you will have to go to ADS with the references above.

Also, I cannot figure out how these terms

11. I just copied it into Wolframalpha and let it do it for me.

Wait, are you using base ten logarithms instead of natural logs?

ETA: or, from your other post, perhaps you're just not familiar with the zeta function?

12. Originally Posted by grapes
I just copied it into Wolframalpha and let it do it for me.
And it nicely gives links to information on the log and zeta functions used. And lets you choose which log function to use.

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Originally Posted by Strange
And it nicely gives links to information on the log and zeta functions used. And lets you choose which log function to use.
I used base 10 log, I looked up the value of the zeta function. Thanks

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What is a magnet moment?

15. Originally Posted by dastardly
What is a magnet moment?
My comic side wants to tell you it's sort of like a senior moment only with magnets instead of seniors, but really it is the force a magnetic field can exert on a current. It is also what is measured with medical MRIs. http://en.wikipedia.org/wiki/Magnetic_moment

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