"BRST quantization and cohomology"의 두 판 사이의 차이

2010년 11월 14일 (일) 08:21 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)

Quantum Group as Semi-infinite Cohomology
- Igor B. Frenkel, Anton M. Zeitlin
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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 * http://en.wikipedia.org/wiki/BRST_quantization
+* http://www.scholarpedia.org/article/Becchi-Rouet-Stora-Tyutin_symmetry
 * Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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+*  Quantum Group as Semi-infinite Cohomology<br>
+** Igor B. Frenkel, Anton M. Zeitlin
 * [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics]
 *  Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras<br>