Anomalous magnetic moment of electron
http://bomber0.myid.net/ (토론)님의 2011년 1월 17일 (월) 12:22 판
introduction
- amplitude = sum of integrals = \(\sum_{n\text{ loops}}\) sum of integrals
- anomalous electron magnetic dipole moment 1.00115965219
- 11 digits match
- as n grows, number of Feynman diagrams grows exponentially
- integrals are becoming difficult
classical magnetic moment
- [1]http://www.wolframalpha.com/input/?i=fine+structure+constant
- [2]http://www.wolframalpha.com/input/?i=1/fine+structure+constant
- A classical electron moving around a nucleus in a circular orbit
- orbital angular momentum, L=m_evr
- magnetic dipole moment, \mu= -evr/2
- where e, m_e, v, and r are the electron´s charge, mass, velocity, and radius, respectively.
- A classical electron of homogeneous mass and charge density rotating about a symmetry axis
- angular momentum, L=(3/5)m_eR^2\Omega
- magnetic dipole moment, \mu= -(3/10)eR^2\Omega, where R and \Omega are the electron´s classical radius and rotating frequency
- gyromagnetic ratio \(\gamma = \mu/L=-e/2m_e\)
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\[\mathbf{\mu}=q\mathbf{S}/m\]
[/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.
- http://docs.google.com/viewer?a=v&q=cache:5hOX9DCrL7sJ:www.physics.ohio-state.edu/~kass/P780_L3_sp03.ppt+anamalous+magnetic+moment+electron+feynman+diagram&hl=ko&gl=us&pid=bl&srcid=ADGEEShmuOjISGxcCejbd6l7kWuRiTY7AtBHwKpZ_Zec4dSTPlJ8kqZSA80srABAl8PEFKnJJVfrawIHlkI0Z9S5wA1ArJMpmMERZp3I3ppK4BN5drRWx4mJi8VTW_wf8xjrs3v1VOqX&sig=AHIEtbTIAIEubf5ZHYPXPv4aE6ImvmxEVw
- [3]http://universe-review.ca/R15-12-QFT.htm
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]
- Toichiro Kinoshita
four-loop diagrams
- 891 diagrams
five-loop Feynman diagrams
- There are 12,672
- http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.html[4]
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 http://oeis.org/A005413
- 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
- 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
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field