"BRST quantization and cohomology"의 두 판 사이의 차이

2011년 4월 23일 (토) 07:39 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
The BRST complex and the cohomology of compact lie algebras
- van Holten, J. W.
Fock representations and BRST cohomology inSL(2) current algebra
- D. Bernard and G. Felder, 1990
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

@@ 1번째 줄: / 1번째 줄: @@
 <h5>introduction</h5>
-*  Gauge theory = principal G-bundle<br>
+* [[Gauge theory]] =<br>
+*  principal G-bundle<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>
@@ 46번째 줄: / 47번째 줄: @@
 <h5 style="margin: 0px; line-height: 2em;">applications</h5>
-*  BRS<br>
+*  BRST approach to minimal models<br>
+*  BRST approach to no-ghost theorem<br>
+*  BRST approach to coset constructions<br>