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

 

 

related items

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

 

 

 

 

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/