"BRST quantization and cohomology"의 두 판 사이의 차이

2011년 10월 4일 (화) 07:39 판

PG minicourse: BRST cohomology (http://empg.maths.ed.ac.uk/Activities/BRST/Notes.pdf , very good introduction)
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)

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

@@ 14번째 줄: / 14번째 줄: @@
-<math>\Lambda_{\infty}</math> semi-infinite form
+* <math>\Lambda_{\infty}</math> semi-infinite form<br>
+* <math>\mathfrak{g}</math> : <math>\mathbb{Z}</math>-graded Lie algebra<br>
-<math>\mathfrak{g}</math> : <math>\mathbb{Z}</math>-graded Lie algebra
+* <math>\sigma</math> : anti-linear automorphism sending <math>\mathfrak{g}_{n}</math> to <math>\mathfrak{g}_{-n}</math><br>
+* <math>H^2(\mathfrak{g})=0</math> (i.e. no non-trivial central extension)<br>
-<math>\sigma</math> : anti-linear automorphism sending \mathfrak{g}_{n} to \mathfrak{g}_{-n}
-H^2(\mathfrak{g})=0 (i.e. no non-trivial central extension)