"BRST quantization and cohomology"의 두 판 사이의 차이

2010년 11월 14일 (일) 06:49 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)

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 *  Gauge theory allows 'local symmetry' which should be ignored to be physical. <br>
 *  This ignoring process leads to the cohomoloy theory.<br>
+*  BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)<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>
@@ 82번째 줄: / 83번째 줄: @@
 <h5 style="margin: 0px; line-height: 2em;">expositions</h5>
-* [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf http://www.math.sciences.univ-nantes.fr/~wagemann/LAlecture.pdf]<br>
+* [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology]<br>
+**  Friedrich Wagemann, 2010-8<br>