Free fermion

introduction

• c=1/2 (for \psi real)
• c=1 (for \psi complex)

 

 

 

action

\(S= \int\!d^2x\, \psi^\dagger \gamma^0 \gamma^\mu \partial_\mu \psi= \int\!d^2z\, \psi^\dagger_R \bar\partial \psi_R + \psi_L^\dagger \bar\partial \psi_L\,\)

 

 

\(\psi(z_1)\psi(z_2) \sim \frac{1}{(z_1 - z_2)}\)

 

 

energy-momentum tensor

• \(T(z)=-\frac{1}{2}:\psi(z)\partial \psi(z):=-\frac{1}{2}\left(\lim_{w\to z}\psi(z)\partial \psi(z)+\frac{1}{(z-w)^2}\right)\)

 

 

 

 

history

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

 

 

related items

• free massless boson
• ghost fields