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 quantization of QED

• 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