Yang-Mills Theory(Non-Abelian gauge theory)

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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.
Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects Ambar N. Sengupta
Introduction to Yang-Mills theories
http://michaelnielsen.org/blog/yang_mills.pdf
History of Yang-Mills theory and wishful thinking The Reference Frame
Electromagnetic duality for children
What Is Geometry? Shiing-Shen Chern, The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686
Introduction to gauge theories and the Standard Model CERN video lectures

articles

Huang, Teng. “Yang-Mills Connections on \(G_{2}\)-Manifolds and Calabi-Yau 3-Folds.” arXiv:1502.02090 [math-Ph], February 6, 2015. http://arxiv.org/abs/1502.02090.
Yang-Mills Theory and Geometry, Donaldson
C. N. Yang and R. L. Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96, 191 - 195 (1954)

encyclopedia

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ID : 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'}]

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