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

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3번째 줄: 3번째 줄:
 
* amplitude = sum of integrals = <math>\sum_{n\text{ loops}}</math> sum of integrals
 
* amplitude = sum of integrals = <math>\sum_{n\text{ loops}}</math> sum of integrals
 
* anomalous electron magnetic dipole moment 1.00115965219
 
* anomalous electron magnetic dipole moment 1.00115965219
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* 11 digits match
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* theoretical computation matches 11 digits with experiments
 
* as n grows, number of Feynman diagrams grows exponentially
 
* as n grows, number of Feynman diagrams grows exponentially
 
* integrals are becoming difficult
 
* integrals are becoming difficult
13번째 줄: 13번째 줄:
 
<h5>classical magnetic moment</h5>
 
<h5>classical magnetic moment</h5>
  
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* [http://www.wolframalpha.com/input/?i=fine+structure+constant ]http://www.wolframalpha.com/input/?i=fine+structure+constant
 
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* [http://www.wolframalpha.com/input/?i=1/fine+structure+constant ]http://www.wolframalpha.com/input/?i=1/fine+structure+constant
 
 
*  A classical electron moving around a nucleus in a circular orbit<br>
 
*  A classical electron moving around a nucleus in a circular orbit<br>
 
** orbital angular momentum, L=m_evr
 
** orbital angular momentum, L=m_evr
23번째 줄: 21번째 줄:
 
** magnetic dipole moment, \mu= -(3/10)eR^2\Omega, where R and \Omega are the electron´s classical radius and rotating frequency
 
** magnetic dipole moment, \mu= -(3/10)eR^2\Omega, where R and \Omega are the electron´s classical radius and rotating frequency
 
* gyromagnetic ratio <math>\gamma = \mu/L=-e/2m_e</math>
 
* gyromagnetic ratio <math>\gamma = \mu/L=-e/2m_e</math>
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33번째 줄: 29번째 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>
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*  classical vs quantum<br>[/pages/3589069/attachments/4562673 2004329152457_150.gif]<br>
  
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[/pages/3589069/attachments/4562673 2004329152457_150.gif]
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 The g factor sets the strength of an electron’s interaction with a magnetic field.
 
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In classical physics (left) magnetic lines of force (perpendicular to the page) induce a curvature in the electron’s path.
 
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In quantum electrodynamics (right) the electron interacts with the field by emitting or absorbing a photon.
 
  
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The event is represented in a Feynman diagram, where space extends along the horizontal axis and time moves up the vertical axis.
+
* 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://www.wolframalpha.com/input/?i=fine+structure+constant
 +
* http://www.wolframalpha.com/input/?i=1/fine+structure+constant
  
 
 
 
 

2011년 1월 17일 (월) 12:27 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
  • 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\[\mathbf{\mu}=q\mathbf{S}/m\]
  • classical vs quantum
    [/pages/3589069/attachments/4562673 2004329152457_150.gif]

 

 

 

 

 

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

 

 

 

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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