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

수학노트
둘러보기로 가기 검색하러 가기
(피타고라스님이 이 페이지를 개설하였습니다.)
 
 
(사용자 3명의 중간 판 40개는 보이지 않습니다)
1번째 줄: 1번째 줄:
 +
==introduction==
  
 +
* This is not a quantum theory.
 +
* This can be regarded as a generalization of theory of electromagetisms., 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
 +
* [[mass gap in Yang-Mills theory]]
 +
 +
 +
 +
 +
==books==
 +
 +
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
 +
* M. Nakahara “Geometry, Topology and Physics”.
 +
* Fifty years of Yang-Mills theory http://books.google.com/books?id=WV57GpYjYREC&pg=PA102&lpg=PA102&dq=weakly+interacting+boson+yang-mills&source=bl&ots=ztMiD8nOgz&sig=nhFiCtCQw2lAodU1zacqg3wueUQ&hl=ko&ei=W1jZTtuZCIqRiALR3c26BA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CHEQ6AEwCQ#v=onepage&q&f=false
 +
 +
 +
 +
 +
 +
==expository==
 +
* Rivière, Tristan. “The Variations of Yang-Mills Lagrangian.” arXiv:1506.04554 [math], June 15, 2015. http://arxiv.org/abs/1506.04554.
 +
* Slavnov, A. A. ‘New Approach to the Quantization of the Yang-Mills Field’. arXiv:1503.03380 [hep-Ph, Physics:hep-Th], 11 March 2015. http://arxiv.org/abs/1503.03380.
 +
* [https://www.math.lsu.edu/%7Esengupta/papers/YMLisbon06Sengup.pdf Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects] Ambar N. Sengupta
 +
* [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]
 +
* http://michaelnielsen.org/blog/yang_mills.pdf
 +
* [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking] The Reference Frame
 +
* [http://www.maths.ed.ac.uk/%7Ejmf/Teaching/EDC.html Electromagnetic duality for children]
 +
* [http://www.jstor.org/stable/2324574 What Is Geometry?] Shiing-Shen Chern, <cite style="line-height: 2em;">The American Mathematical Monthly</cite>, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686
 +
* [http://cds.cern.ch/record/292286?ln=en Introduction to gauge theories and the Standard Model] CERN video lectures
 +
 +
 +
 +
==articles==
 +
* Huang, Teng. “Yang-Mills Connections on <math>G_{2}</math>-Manifolds and Calabi-Yau 3-Folds.” arXiv:1502.02090 [math-Ph], February 6, 2015. http://arxiv.org/abs/1502.02090.
 +
* [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry], Donaldson
 +
* C. N. Yang and R. L. Mills, [http://dx.doi.org/10.1103/PhysRev.96.191 Conservation of Isotopic Spin and Isotopic Gauge Invariance], Phys. Rev. '''96''', 191 - 195 (1954)
 +
 +
 +
 +
 +
 +
==encyclopedia==
 +
 +
* http://en.wikipedia.org/wiki/Yang-Mills_theory
 +
* http://en.wikipedia.org/wiki/Gauge_theory
 +
* http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory
 +
 +
[[분류:개인노트]]
 +
[[분류:math and physics]]
 +
[[분류:gauge theory]]
 +
[[분류:migrate]]
 +
 +
==메타데이터==
 +
===위키데이터===
 +
* ID :  [https://www.wikidata.org/wiki/Q1192873 Q1192873]
 +
===Spacy 패턴 목록===
 +
* [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
 +
* [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
 +
* [{'LOWER': 'non'}, {'LOWER': '-'}, {'LOWER': 'abelian'}, {'LOWER': 'gauge'}, {'LEMMA': 'theory'}]

2021년 2월 17일 (수) 02:09 기준 최신판

introduction

  • This is not a quantum theory.
  • This can be regarded as a generalization of theory of electromagetisms., 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



books



expository


articles



encyclopedia

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
  • [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
  • [{'LOWER': 'non'}, {'LOWER': '-'}, {'LOWER': 'abelian'}, {'LOWER': 'gauge'}, {'LEMMA': 'theory'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Yang-Mills_Theory(Non-Abelian_gauge_theory)&oldid=51913"