"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
48번째 줄: 48번째 줄:
 
* structure constants are needed
 
* structure constants are needed
 
* self-interaction of gauge fields starts to appear
 
* self-interaction of gauge fields starts to appear
 +
 +
 
 +
 +
 
 +
 +
<h5>Yang-Mills potential</h5>
 +
 +
*  dual role<br>
 +
** a field in space-time
 +
** operator in the isotopic-spin space
  
 
 
 
 
76번째 줄: 86번째 줄:
 
<h5>expository</h5>
 
<h5>expository</h5>
  
−
* [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]<br>http://michaelnielsen.org/blog/yang_mills.pdf<br>
+
* Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects Ambar N. Sengupta
 +
*   <br>[http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]<br>http://michaelnielsen.org/blog/yang_mills.pdf<br>
 
* [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking]<br>
 
* [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking]<br>
 
** The Reference Frame
 
** The Reference Frame

2011년 9월 23일 (금) 06:36 판

introduction
  • This is not a quantum theory.
  • This can be regarded as a generalization of electromagetics., i.e. bundle + connections
  • looks like the coordinate invariance of gravity theory
  • Gauge theory
  • Usually, non-abelian gauge theory is called the YM theory.
    • QCD is one example.

 

 

basic concepts
  • connection
  • curvature

 

 

original Yang-Mills model
  • three kinds of photon
    • one ordinary photon
    • two electrically charged photons with spin 1 which is physically impossible to exist
  • massless gauge fields
    • for example, electromagnetic field(the only example at that time)

 

 

weak force

 

 

 

recipe
  • prepare Dirac fields
  • start with the free Dirac Lagrangian
  • we demand the Lagrangian to be invariant under the SU(N) local gauge transformations
  • structure constants are needed
  • self-interaction of gauge fields starts to appear

 

 

Yang-Mills potential
  • dual role
    • a field in space-time
    • operator in the isotopic-spin space

 

 

quantization of Yang-Mills theory
  • We want to quantize this theory.
  • standard model is a quantized version of a Yang-Mills theory of classical fields

 

 

books

 

 

expository

 

articles

 

 

encyclopedia

 

 

블로그
원본 주소 "https://wiki.mathnt.net/index.php?title=Yang-Mills_Theory(Non-Abelian_gauge_theory)&oldid=35804"