BRST quantization and cohomology

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)

 

 

 

related items

• 물리학과 cohomology
  
• Homological algebra
  
•  
  

 

 

books

• 찾아볼 수학책
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

[1]

 

blogs

• http://www.math.columbia.edu/~woit/notesonbrst.pdf
• http://www.math.columbia.edu/~woit/wordpress/?cat=12
• Notes on BRST I: Representation Theory and Quantum Mechanics
• Notes on BRST II: Lie Algebra Cohomology, Physicist’s Version
• Notes on BRST III: Lie Algebra Cohomology
• Notes on BRST IV: Lie Algebra Cohomology for Semi-simple Lie Algebras
• Notes on BRST V: Highest Weight Theory

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

expositions

• Introduction to Lie algebra cohomology with a view towards BRST cohomology
  
  • Friedrich Wagemann, 2010-8
    

 

 

articles

• 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
• 논문정리
• http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html

• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=