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

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==introduction==
  
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* This is not a quantum theory.
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* This can be regarded as a generalization of theory of electromagetisms., i.e. bundle + connections
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* looks like the coordinate invariance of gravity theory
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* [[Gauge theory]]
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*  Usually, non-abelian gauge theory is called the YM theory.
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** QCD is one example.
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==basic concepts==
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* connection
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* curvature
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==original Yang-Mills model==
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*  three kinds of photon
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** one ordinary photon
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** two electrically charged photons with spin 1 which is physically impossible to exist
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*  massless gauge fields
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** for example, electromagnetic field(the only example at that time)
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==weak force==
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==recipe==
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* prepare Dirac fields
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* start with the free Dirac Lagrangian
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* we demand the Lagrangian to be invariant under the SU(N) local gauge transformations
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* structure constants are needed
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* self-interaction of gauge fields starts to appear
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==Yang-Mills potential==
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*  dual role
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** a field in space-time
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** operator in the isotopic-spin space
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==quantization of Yang-Mills theory==
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* We want to quantize this theory.
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* standard model is a quantized version of a Yang-Mills theory of classical fields
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* [[mass gap in Yang-Mills theory]]
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==books==
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* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
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* M. Nakahara “Geometry, Topology and Physics”.
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* 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
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==expository==
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* Rivière, Tristan. “The Variations of Yang-Mills Lagrangian.” arXiv:1506.04554 [math], June 15, 2015. http://arxiv.org/abs/1506.04554.
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* 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.
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* [https://www.math.lsu.edu/%7Esengupta/papers/YMLisbon06Sengup.pdf Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects] Ambar N. Sengupta
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* [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]
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* http://michaelnielsen.org/blog/yang_mills.pdf
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* [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking] The Reference Frame
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* [http://www.maths.ed.ac.uk/%7Ejmf/Teaching/EDC.html Electromagnetic duality for children]
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* [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
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* [http://cds.cern.ch/record/292286?ln=en Introduction to gauge theories and the Standard Model] CERN video lectures
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==articles==
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* 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.
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* [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry], Donaldson
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* 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)
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Yang-Mills_theory
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* http://en.wikipedia.org/wiki/Gauge_theory
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* http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory
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[[분류:개인노트]]
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[[분류:math and physics]]
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[[분류:gauge theory]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q1192873 Q1192873]
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===Spacy 패턴 목록===
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* [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
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* [{'LOWER': 'yang'}, {'OP': '*'}, {'LOWER': 'mills'}, {'LEMMA': 'theory'}]
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* [{'LOWER': 'non'}, {'LOWER': '-'}, {'LOWER': 'abelian'}, {'LOWER': 'gauge'}, {'LEMMA': 'theory'}]

2021년 2월 17일 (수) 03:09 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'}]
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