Constrained system : U(1) pure gauge theory

introduction

• U(1) pure gauge theory  : theory of light (without matter)
  \(\mathcal{L}_{\text{free}} = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)
  
• quantization of the photon field http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT4.pdf
  
  • fix the gauge
  • quantize unconstrained system
  • gives physical and unphysical states (negative norm states)
  • impose the constraint condition to remove negative norm states
  • we get a Hilbert space of physical states
• Gupta-Bleuler Method http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism

 

 

 

 

remark

if matter exists, we get QED

\(\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• no-ghost theorem and the construction of moonshine module and monster Lie algbera

 

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• http://eom.springer.de
• http://www.proofwiki.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

 

• 2011년 books and articles
• http://library.nu/search?q=
• http://library.nu/search?q=

 

 

 

 

articles

 

• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://www.pdf-search.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://math.stackexchange.com/search?q=
• http://physics.stackexchange.com/search?q=

 

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
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