"BRST quantization and cohomology"의 두 판 사이의 차이

2010년 11월 14일 (일) 06:54 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)

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
논문정리
http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
http://www.zentralblatt-math.org/zmath/en/
http://pythagoras0.springnote.com/
http://math.berkeley.edu/~reb/papers/index.html

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+*  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