"BRST quantization and cohomology"의 두 판 사이의 차이

2010년 11월 30일 (화) 15:37 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

@@ 39번째 줄: / 39번째 줄: @@
 * [http://bolvan.ph.utexas.edu/%7Evadim/Classes/2008f.homeworks/brst.pdf http://bolvan.ph.utexas.edu/~vadim/Classes/2008f.homeworks/brst.pdf]<br>
 * [http://www.nuclecu.unam.mx/%7Echryss/papers/brst_final.pdf http://www.nuclecu.unam.mx/~chryss/papers/brst_final.pdf]<br>
+<h5 style="margin: 0px; line-height: 2em;">applications</h5>
+*  BRS<br>
@@ 97번째 줄: / 105번째 줄: @@
 *  The BRST complex and the cohomology of compact lie algebras<br>
 ** van Holten, J. W.
-* Fock representations and BRST cohomology inSL(2) current algebra
+* [http://dx.doi.org/10.1007/BF02096498 Fock representations and BRST cohomology inSL(2) current algebra]<br>
-* <br> D. Bernard and G. Felder
+** D. Bernard and G. Felder, 1990
 * [http://dx.doi.org/10.1007/BF01466770 BRST cohomology in classical mechanics]
 *  Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras<br>
@@ 104번째 줄: / 112번째 줄: @@
 * [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
+* http://dx.doi.org/10.1007/BF02096498