"BRST quantization and cohomology"의 두 판 사이의 차이

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6번째 줄: 6번째 줄:
 
*  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>
 
*  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>
 
*  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>
 
*  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>
14번째 줄: 14번째 줄:
 
 
 
 
  
\Lambda_{\infty} semi-infinite form
+
<math>\Lambda_{\infty}</math> semi-infinite form
  
\mathfrak{g} : \mathbb{Z}-graded Lie algebra
+
<math>\mathfrak{g}</math> : <math>\mathbb{Z}</math>-graded Lie algebra
  
\sigma : anti-linear automorphism sending \mathfrak{g}_{n} to \mathfrak{g}_{-n}
+
<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)
 
H^2(\mathfrak{g})=0 (i.e. no non-trivial central extension)

2011년 9월 27일 (화) 07:52 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

 

 

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encyclopedia

 

[1]

 

 

expositions

 

 

articles

 

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