"BRST quantization and cohomology"의 두 판 사이의 차이

2010년 11월 14일 (일) 08:10 판

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)

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/BF01466770

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+<h5 style="margin: 0px; line-height: 2em;">nilpotency of BRST operator</h5>
+[http://bolvan.ph.utexas.edu/%7Evadim/Classes/2008f.homeworks/brst.pdf http://bolvan.ph.utexas.edu/~vadim/Classes/2008f.homeworks/brst.pdf]
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 * [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology]<br>
 **  Friedrich Wagemann, 2010-8<br>
+* [http://empg.maths.ed.ac.uk/Activities/BRST/ PG minicourse: BRST cohomology]<br>
@@ 74번째 줄: / 81번째 줄: @@
 <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>
-* BRST cohomology in classical mechanics 10.1007/BF01466770
+* [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics]
 *  Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras<br>
 ** B. Kostant, S. Sternberg, Ann. Physics 176 (1987) 49–113
 * [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
+* http://dx.doi.org/10.1007/BF01466770