BRST quantization and cohomology

수학노트
http://bomber0.myid.net/ (토론)님의 2011년 9월 27일 (화) 07:32 판
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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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