"Gauge theory"의 두 판 사이의 차이
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* [[QED]]<br> | * [[QED]]<br> | ||
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* manifold <math>\mathbb R^{1,3}</math> and having a vector bundle gives a connection<br> | * manifold <math>\mathbb R^{1,3}</math> and having a vector bundle gives a connection<br> | ||
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| − | <h5 style=" | + | <h5 style="margin: 0px; line-height: 2em;">Principal G-bundle</h5> |
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| − | <h5 style=" | + | <h5 style="margin: 0px; line-height: 2em;">3d Chern-Simons theory</h5> |
* 3d Chern-Simons theory on <math>\Sigma\times \mathbb R^{1}</math> with gauge choice <math>A_0=0</math> is the moduli space of flat connections on <math>\Sigma</math>.<br> | * 3d Chern-Simons theory on <math>\Sigma\times \mathbb R^{1}</math> with gauge choice <math>A_0=0</math> is the moduli space of flat connections on <math>\Sigma</math>.<br> | ||
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| − | <h5 style=" | + | <h5 style="margin: 0px; line-height: 2em;">메모</h5> |
| − | * http://www.google.com/search?hl=en&rls=IBMA,IBMA:2008-50,IBMA:en&q=brief+introduction+to+principal+bundles+connections&aq=f&oq=&aqi= | + | * http://www.google.com/search?hl=en&rls=IBMA,IBMA:2008-50,IBMA:en&q=brief+introduction+to+principal+bundles+connections&aq=f&oq=&aqi=<br> |
| − | <h5 style="line-height: 3.428em | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">관련된 다른 주제들</h5> |
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* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
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| − | * | + | * [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial]<br> |
| + | ** Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399 | ||
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/principal_bundle | * http://en.wikipedia.org/wiki/principal_bundle | ||
| − | * http://en.wikipedia.org/wiki/Connection_(vector_bundle) | + | * [http://en.wikipedia.org/wiki/Connection_%28vector_bundle%29 http://en.wikipedia.org/wiki/Connection_(vector_bundle)] |
* http://viswiki.com/en/ | * http://viswiki.com/en/ | ||
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | * http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | ||
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* 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q= | * 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q= | ||
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2009년 10월 6일 (화) 14:50 판
meaning of the gague invariance
- gauge = measure
- gauge invariance 란 measurement에 있어서의 invariance를 말함
- Lagrangian should be gauge invariant.
examples of renormalizable gauge theory
Abelian gauge theory
- abelian gauge theory has a duality
Non-Abelian gauge theory
differential geometry formulation
- manifold \(\mathbb R^{1,3}\) and having a vector bundle gives a connection
- connection \(A\) = special kind of 1-form
- \(dA\) = 2-form which measures the electromagnetic charge
- Then the Chern class measures the magnetic charge.
Principal G-bundle
3d Chern-Simons theory
- 3d Chern-Simons theory on \(\Sigma\times \mathbb R^{1}\) with gauge choice \(A_0=0\) is the moduli space of flat connections on \(\Sigma\).
- analogy with class field theory
- replace \(\Sigma\) by \(spec O_K\)
- then flat connection on \(spec O_K\) is given by Homomorphism group the absolute Galois group Gal(\barQ/K)->U(1)
- Now from An's article,
메모
관련된 다른 주제들
표준적인 도서 및 추천도서
- 찾아볼 수학책
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
참고할만한 자료
- Quantum field theory and the Jones polynomial
- Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399
- http://www.zentralblatt-math.org/zmath/en/
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/principal_bundle
- http://en.wikipedia.org/wiki/Connection_(vector_bundle)
- http://viswiki.com/en/
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=
블로그
- 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
- 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=