"BRST quantization and cohomology"의 두 판 사이의 차이

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<h5>introduction</h5>
 
<h5>introduction</h5>
  
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* [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>
 
* [[Gauge theory]] = principal G-bundle<br>
 
* [[Gauge theory]] = principal G-bundle<br>
*  We require a quantization of gauge theory.<br>
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*  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>
+
*  BRST quantization is one way to quantize the theory and is a part of path integral<br>
*  Gauge theory allows 'local symmetry' which should be ignored to be physical<br>
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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>
 
*  This ignoring process leads to the cohomoloy theory.<br>
 
*  BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)<br>
 
*  BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)<br>
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H^2(\mathfrak{g})=0 (i.e. no non-trivial central extension)
 
H^2(\mathfrak{g})=0 (i.e. no non-trivial central extension)
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91번째 줄: 98번째 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://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 intro)<br>
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* [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>
  
 
 
 
 

2011년 9월 27일 (화) 06:32 판

introduction
  • 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)

 

 

 

 

 

ghost variables

 

 

 

nilpotency of BRST operator

 

 

applications
  • BRST approach to minimal models
  • BRST approach to no-ghost theorem
  • BRST approach to coset constructions

 

 

 

related items

 

 

books

 

 

encyclopedia

 

[1]

 

 

expositions

 

 

articles

 

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