"BRST quantization and cohomology"의 두 판 사이의 차이
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<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | * [[Gauge theory]] = | + | * [[Gauge theory]] = principal G-bundle<br> |
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* We require a quantization of gauge theory.<br> | * We require a quantization of gauge theory.<br> | ||
* BRST quantization is one way to quantize the theory and is a part of path integral.<br> | * BRST quantization is one way to quantize the theory and is a part of path integral.<br> | ||
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* [[물리학과 cohomology]]<br> | * [[물리학과 cohomology]]<br> | ||
* [[homological algebra|Homological algebra]]<br> | * [[homological algebra|Homological algebra]]<br> | ||
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<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%;">books</h5> | <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%;">books</h5> | ||
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* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
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<h5 style="margin: 0px; line-height: 2em;">expositions</h5> | <h5 style="margin: 0px; line-height: 2em;">expositions</h5> | ||
| − | * [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology] | + | * [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology] ,Friedrich Wagemann, 2010-8<br> |
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* [http://empg.maths.ed.ac.uk/Activities/BRST/ PG minicourse: BRST cohomology]<br> | * [http://empg.maths.ed.ac.uk/Activities/BRST/ PG minicourse: BRST cohomology]<br> | ||
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<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%;">articles</h5> | <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%;">articles</h5> | ||
| − | * | + | * Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology |
| − | * | + | * van Holten, J. W., The BRST complex and the cohomology of compact lie algebras |
| − | + | * D. Bernard and G. Felder, 1990, [http://dx.doi.org/10.1007/BF02096498 Fock representations and BRST cohomology inSL(2) current algebra] | |
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* [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics] | * [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics] | ||
| − | * | + | * Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras, B. Kostant, S. Sternberg, Ann. Physics 176 (1987) 49–113 |
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* [http://www.pnas.org/content/83/22/8442.abstract Semi-infinite cohomology and string theory]<br> | * [http://www.pnas.org/content/83/22/8442.abstract Semi-infinite cohomology and string theory]<br> | ||
** I. B. Frenkel,. H. Garland, and. G. J. Zuckerman, PNAS November 1, 1986 vol. 83 no. 22 8442-8446 | ** I. B. Frenkel,. H. Garland, and. G. J. Zuckerman, PNAS November 1, 1986 vol. 83 no. 22 8442-8446 | ||
2011년 4월 23일 (토) 06:59 판
introduction
- Gauge theory = principal G-bundle
- We require a quantization of gauge theory.
- BRST quantization is one way to quantize the theory and is a part of path integral.
- Gauge theory allows 'local symmetry' which should be ignored to be physical.
- This ignoring process leads to the cohomoloy theory.
- BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)
- the conditions D = 26 and α0 = 1 for the space-time dimension D and the zero-intercept α0 of leading trajectory are required by the nilpotency QB2 = 0 of the BRS charge
\Lambda_{\infty} semi-infinite form
\mathfrak{g} : \mathbb{Z}-graded Lie algebra
\sigma : anti-linear automorphism sending \mathfrak{g}_{n} to \mathfrak{g}_{-n}
H^2(\mathfrak{g})=0 (i.e. no non-trivial central extension)
ghost variables
nilpotency of BRST operator
- http://bolvan.ph.utexas.edu/~vadim/Classes/2008f.homeworks/brst.pdf
- http://www.nuclecu.unam.mx/~chryss/papers/brst_final.pdf
applications
- BRST approach to minimal models
- BRST approach to no-ghost theorem
- BRST approach to coset constructions
books
encyclopedia
- http://en.wikipedia.org/wiki/BRST_quantization
- http://www.scholarpedia.org/article/Becchi-Rouet-Stora-Tyutin_symmetry
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
expositions
- Introduction to Lie algebra cohomology with a view towards BRST cohomology ,Friedrich Wagemann, 2010-8
- PG minicourse: BRST cohomology
articles
- Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology
- van Holten, J. W., The BRST complex and the cohomology of compact lie algebras
- D. Bernard and G. Felder, 1990, Fock representations and BRST cohomology inSL(2) current algebra
- BRST cohomology in classical mechanics
- Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras, B. Kostant, S. Sternberg, Ann. Physics 176 (1987) 49–113
- Semi-infinite cohomology and string theory
- I. B. Frenkel,. H. Garland, and. G. J. Zuckerman, PNAS November 1, 1986 vol. 83 no. 22 8442-8446
- http://dx.doi.org/10.1007/BF02096498
blogs
- http://www.math.columbia.edu/~woit/notesonbrst.pdf
- http://www.math.columbia.edu/~woit/wordpress/?cat=12
- Notes on BRST I: Representation Theory and Quantum Mechanics
- Notes on BRST II: Lie Algebra Cohomology, Physicist’s Version
- Notes on BRST III: Lie Algebra Cohomology
- Notes on BRST IV: Lie Algebra Cohomology for Semi-simple Lie Algebras
- Notes on BRST V: Highest Weight Theory
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