BRST quantization and cohomology

수학노트
http://bomber0.myid.net/ (토론)님의 2010년 11월 17일 (수) 19:00 판 (피타고라스님이 이 페이지의 이름을 BRST cohomology로 바꾸었습니다.)
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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

 

 

related items

 

 

books

 

 

encyclopedia

 

[1]

 

 

expositions

 

 

articles
  • Quantum Group as Semi-infinite Cohomology
    • Igor B. Frenkel, Anton M. Zeitlin
  • The BRST complex and the cohomology of compact lie algebras
    • van Holten, J. W.
  • Fock representations and BRST cohomology inSL(2) current algebra

  • D. Bernard and G. Felder
  • BRST cohomology in classical mechanics
  • Symplectic Reduction, BRS Cohomology, and Infinite-Dimensional Clifford algebras
    • B. Kostant, S. Sternberg, Ann. Physics 176 (1987) 49–113
  • Semi-infinite cohomology and string theory
    • I. B. Frenkel,. H. Garland, and. G. J. Zuckerman, PNAS November 1, 1986 vol. 83 no. 22 8442-8446
  • http://dx.doi.org/10.1007/BF01466770

 

blogs

 

 

 

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