"Anomalous magnetic moment of electron"의 두 판 사이의 차이

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32번째 줄: 32번째 줄:
 
* In quantum electrodynamics (right) the electron interacts with the field by emitting or absorbing a photon.
 
* 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.
 
* The event is represented in a Feynman diagram, where space extends along the horizontal axis and time moves up the vertical axis.
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* <math>g=2(1+c_1\frac{\alpha}{2\pi}+c_2(\frac{\alpha}{2\pi})^2+c_3(\frac{\alpha}{2\pi})^3+\cdots)</math>
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* <math>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</math>
 
* http://www.wolframalpha.com/input/?i=fine+structure+constant
 
* http://www.wolframalpha.com/input/?i=fine+structure+constant
 
* http://www.wolframalpha.com/input/?i=1/fine+structure+constant
 
* http://www.wolframalpha.com/input/?i=1/fine+structure+constant
49번째 줄: 49번째 줄:
 
*  1 one-loop diagram<br>[/pages/7141159/attachments/4563145 2004329152921_150.gif]<br>
 
*  1 one-loop diagram<br>[/pages/7141159/attachments/4563145 2004329152921_150.gif]<br>
 
*  Feynman, Julian Schwinger, Sin-Itiro Tomonaga and Freeman Dyson<br>
 
*  Feynman, Julian Schwinger, Sin-Itiro Tomonaga and Freeman Dyson<br>
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*  Schwinger showed that the one-loop contribution to the "anomalous magnetic moment" of the electron is <math>\alpha/{2\pi}</math><br>
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*  Schwinger showed that the one-loop contribution to the "anomalous magnetic moment" of the electron is <math>\alpha/{2\pi}=0.00116\cdots</math><br>
 
* http://www.wolframalpha.com/input/?i=fine+structure+constant%2F%282pi%29<br>
 
* http://www.wolframalpha.com/input/?i=fine+structure+constant%2F%282pi%29<br>
  
128번째 줄: 128번째 줄:
 
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
 
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
  
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* number of Feynman diagrams http://oeis.org/A005413
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* number of Feynman diagrams [http://oeis.org/A005413 ]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/Anomalous_magnetic_dipole_moment
 
* http://en.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/

2011년 1월 17일 (월) 13:09 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

 

 

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\[\mathbf{\mu}=q\mathbf{S}/m\]
  • 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

 

 

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

 

 

 

anaomalous muon magnetic dipole moment

 

 

memo

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

expositions

 

 

articles

 

 

question and answers(Math Overflow)

 

 

blogs

 

 

experts on the field

 

 

links
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