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

2011년 12월 3일 (토) 10:02 판

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.

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)

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

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

Yang-Mills Theory and Geometry
- Donaldson
What Is Geometry?
- Shiing-Shen Chern, The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686
C. N. Yang and R. L. Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96, 191 - 195 (1954)

@@ 76번째 줄: / 76번째 줄: @@
 * 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
 * [[2009년 books and articles|찾아볼 수학책]]
 * http://gigapedia.info/1/
@@ 104번째 줄: / 105번째 줄: @@
 * [http://www.jstor.org/stable/2324574 What Is Geometry?]<br>
 ** 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
+* 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)