"Anomalous magnetic moment of electron"의 두 판 사이의 차이
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| 14번째 줄: | 14번째 줄: | ||
* read [[spin system and Pauli exclusion principle|spin system]] first | * read [[spin system and Pauli exclusion principle|spin system]] first | ||
| − | * gyromagnetic ratio <math>\gamma = \mu/L=-e/2m_e</math><br>[/pages/7141159/attachments/4562863 I15-62-g20.jpg]<br> | + | * gyromagnetic ratio is defined as "magnetic dipole moment"/"angular momentum"<br><math>\gamma = \mu/L=-e/2m_e</math><br>[/pages/7141159/attachments/4562863 I15-62-g20.jpg]<br> |
* pictures from [http://universe-review.ca/R15-12-QFT.htm#g2 Gyromagnetic Ratio and Anomalous Magnetic Moment] | * pictures from [http://universe-review.ca/R15-12-QFT.htm#g2 Gyromagnetic Ratio and Anomalous Magnetic Moment] | ||
| 24번째 줄: | 24번째 줄: | ||
* In Dirac’s theory a point like spin 1/2 object of electric charge q and mass m has a magnetic moment: <math>\mathbf{\mu}=q\mathbf{S}/m</math> | * In Dirac’s theory a point like spin 1/2 object of electric charge q and mass m has a magnetic moment: <math>\mathbf{\mu}=q\mathbf{S}/m</math> | ||
| − | * so the Bohr magneton of the electron becomes<br><math>\mu_\mathrm{B} = {{e \hbar} \over {2 m_\mathrm{e}}}</math><br> | + | * so the Bohr magneton of the electron ([http://en.wikipedia.org/wiki/Bohr_magneton%29 http://en.wikipedia.org/wiki/Bohr_magneton)] becomes<br><math>\mu_\mathrm{B} = {{e \hbar} \over {2 m_\mathrm{e}}}</math> since the spin of the electron is <math>S=\frac{\hbar}{2}</math><br> |
| − | * spin magnetic moment involves the spin g-factor<br><math>\vec{\mu}_S \ = g_e \mu_\mathrm{B} \frac{\vec{S}}{\hbar}=g\frac{e}{2 | + | |
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| + | * actual spin magnetic moment of the electron involves the spin g-factor (gyromagnetic ratio)<br><math>\vec{\mu}_S \ = g_e \mu_\mathrm{B} \frac{\vec{S}}{\hbar}=g\frac{e}{2 m_{e}} \ \vec{S}</math><br> | ||
* classical vs quantum<br>[/pages/3589069/attachments/4562673 2004329152457_150.gif]<br> | * classical vs quantum<br>[/pages/3589069/attachments/4562673 2004329152457_150.gif]<br> | ||
2011년 1월 17일 (월) 13:27 판
introduction
- amplitude = sum of integrals = \(\sum_{n\text{ loops}}\) sum of integrals
- anomalous electron magnetic dipole moment 1.00115965219
- theoretical computation matches 11 digits with experiments
- as n grows, number of Feynman diagrams grows exponentially
- integrals are becoming difficult
classical magnetic moment
- read spin system first
- gyromagnetic ratio is defined as "magnetic dipole moment"/"angular momentum"
\(\gamma = \mu/L=-e/2m_e\)
[/pages/7141159/attachments/4562863 I15-62-g20.jpg] - pictures from Gyromagnetic Ratio and Anomalous Magnetic Moment
anamalous electron magnetic dipole moment
- In Dirac’s theory a point like spin 1/2 object of electric charge q and mass m has a magnetic moment\[\mathbf{\mu}=q\mathbf{S}/m\]
- so the Bohr magneton of the electron (http://en.wikipedia.org/wiki/Bohr_magneton) becomes
\(\mu_\mathrm{B} = {{e \hbar} \over {2 m_\mathrm{e}}}\) since the spin of the electron is \(S=\frac{\hbar}{2}\)
- actual spin magnetic moment of the electron involves the spin g-factor (gyromagnetic ratio)
\(\vec{\mu}_S \ = g_e \mu_\mathrm{B} \frac{\vec{S}}{\hbar}=g\frac{e}{2 m_{e}} \ \vec{S}\) - classical vs quantum
[/pages/3589069/attachments/4562673 2004329152457_150.gif]
- The g factor sets the strength of an electron’s interaction with a magnetic field.
- In classical physics (left) magnetic lines of force (perpendicular to the page) induce a curvature in the electron’s path.
- In quantum electrodynamics (right) the electron interacts with the field by emitting or absorbing a photon.
- The event is represented in a Feynman diagram, where space extends along the horizontal axis and time moves up the vertical axis.
- \(g/2=1+c_1\frac{\alpha}{2\pi}+c_2(\frac{\alpha}{2\pi})^2+c_3(\frac{\alpha}{2\pi})^3+\cdots=1.00115965219+\cdots\)
- http://www.wolframalpha.com/input/?i=fine+structure+constant
- http://www.wolframalpha.com/input/?i=1/fine+structure+constant
tree level and one-loop diagrams
- 1 one-loop diagram
[/pages/7141159/attachments/4563145 2004329152921_150.gif] - Feynman, Julian Schwinger, Sin-Itiro Tomonaga and Freeman Dyson
- Schwinger showed that the one-loop contribution to the "anomalous magnetic moment" of the electron is \(\alpha/{2\pi}=0.00116\cdots\)
- http://www.wolframalpha.com/input/?i=fine+structure+constant%2F%282pi%29
two-loop diagrams
- 7 two-loop diagrams
[/pages/3589069/attachments/4562669 2004329153354_150.gif]
[/pages/7141159/attachments/4562733 I15-62-g2c.jpg]
three-loop diagrams
- 72 three-loop diagrams
- [/pages/3589069/attachments/4562671 200432915395_150.gif]
- Kinoshita, Toichiro. 1995. New Value of the alpha^{3} Electron Anomalous Magnetic Moment. Physical Review Letters 75, no. 26 (December 25): 4728. doi:10.1103/PhysRevLett.75.4728.
four-loop diagrams
- 891 diagrams
five-loop Feynman diagrams
- There are 12,672
- http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.html[1]
anaomalous muon magnetic dipole moment
- anaomalous muon magnetic dipole moment is still unknown
- http://eskesthai.blogspot.com/2010/12/muon.html
memo
history
encyclopedia
- number of Feynman diagrams [2]http://oeis.org/A005413
- http://en.wikipedia.org/wiki/G-factor_%28physics%29
- http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- Brian Hayes, “g-OLOGY,” American Scientist 92, no. 3 (2004): 212. http://www.americanscientist.org/issues/num2/g-ology/1
articles
- Broadhurst, D. J, and D. Kreimer. 1996. Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops. hep-th/9609128 (September 16). doi:doi:10.1016/S0370-2693(96)01623-1. http://arxiv.org/abs/hep-th/9609128.
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
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- http://ncatlab.org/nlab/show/HomePage
experts on the field