"BRST quantization and cohomology"의 두 판 사이의 차이

2011년 10월 4일 (화) 08:05 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)

Introduction to Lie algebra cohomology with a view towards BRST cohomology ,Friedrich Wagemann, 2010-8
PG minicourse: BRST cohomology (http://empg.maths.ed.ac.uk/Activities/BRST/Notes.pdf José Figueroa-O’Farrill 2006
D'Hooker, E., Phong, D.H.: The geometry of string perturbation theory. Rev. Mod. Phys. 60,. 917-1065 (1988)

Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology
van Holten, J. W., The BRST complex and the cohomology of compact lie algebras
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/10.1007/BF02096498

@@ 9번째 줄: / 9번째 줄: @@
 *  re-packaging of Faddeev-Popov quantization<br>
 *  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<br>
+<h5 style="margin: 0px; line-height: 2em;">gauge fixing</h5>
@@ 17번째 줄: / 27번째 줄: @@
 * [[Faddeev–Popov ghost fields|ghost fields]]<br>
@@ 99번째 줄: / 113번째 줄: @@
 * [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology] ,Friedrich Wagemann, 2010-8<br>
-* [http://empg.maths.ed.ac.uk/Activities/BRST/ PG minicourse: BRST cohomology] (http://empg.maths.ed.ac.uk/Activities/BRST/Notes.pdf , very good introduction)<br>
+* [http://empg.maths.ed.ac.uk/Activities/BRST/ PG minicourse: BRST cohomology] (http://empg.maths.ed.ac.uk/Activities/BRST/Notes.pdf  José Figueroa-O’Farrill 2006<br>
+*  D'Hooker, E., Phong, D.H.: The geometry of string perturbation theory. Rev. Mod. Phys. 60,. 917-1065 (1988)<br>