"BRST quantization and cohomology"의 두 판 사이의 차이

2011년 10월 4일 (화) 08:22 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”)
re-packaging of Faddeev-Popov quantization
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)

Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology
J.W., van Holten. 1990. “The BRST complex and the cohomology of compact lie algebras”. Nuclear Physics B 339 (1) (7월 23): 158-176. doi:10.1016/0550-3213(90)90537-N
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
I. B. Frenkel,. H. Garland, and. G. J. Zuckerman, PNAS November 1, 1986 vol. 83 no. 22 8442-8446, Semi-infinite cohomology and string theory
http://dx.doi.org/10.1103/RevModPhys.60.917

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+<h5 style="margin: 0px; line-height: 2em;">path integral</h5>
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 * Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology
-* J.W., van Holten. 1990. “The BRST complex and the cohomology of compact lie algebras”. <em>Nuclear Physics B</em> 339 (1) (7월 23): 158-176. doi:10.1016/0550-3213(90)90537-N.
+*   <br> J.W., van Holten. 1990. “The BRST complex and the cohomology of compact lie algebras”. <em>Nuclear Physics B</em> 339 (1) (7월 23): 158-176. doi:[http://dx.doi.org/10.1016/0550-3213%2890%2990537-N 10.1016/0550-3213(90)90537-N]<br>
 * D. Bernard and G. Felder, 1990, [http://dx.doi.org/10.1007/BF02096498 Fock representations and BRST cohomology inSL(2) current algebra]
 * [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics]