Applications of Light-Front Dynamics in Hadron Physics 1. What is ...

Canonical Quantization
Simple 1+1 dim QFT:
L = 1 2 ! µ! ! µ ! " 1 2 m2 ! 2
L = C #
$
2 (! ˆ+!) 2 " (! ˆ"!) 2
%
& + S(! ˆ+!)(! ˆ"!)" 1 2 m2 ! 2
C = cos(2!), S = sin(2!)
! (x) = !L
!(! 0
") = !0 "
! (x) = C! ˆ+" + S! ˆ""
Conjugate field:
Equal-time quantization:
[! (x),"(y)] x 0 =y 0 = !i#(x 3 ! y 3 )
[! (x),"(y)] x ˆ+ =y ˆ+ = !i#(x ˆ! ! y ˆ! )