nLab
state-field correspondence

A field operator ϕ\phi in a quantum field theory with a distinguished vacuum vector |0|0\rangle defines its incoming state as the |phi in:=U(0,)ϕ|0|phi_{in}\rangle :=U(0,-\infty)\phi |0\rangle i.e. as the limit when time goes to infinity of the state ϕ|0\phi|0\rangle, here U(t 1,t 2)U(t_1,t_2) is the evolution operator from t 1t_1 to t 2t_2 (which may be written as U(t 2t 1)U(t_2-t_1) when the Hamiltonian is time-independent), which is by definition the inverse of U(t 2,t 1)U(t_2,t_1) for t 2>t 1t_2\gt t_1. The assignment ϕ|phi in\phi\mapsto |phi_{in}\rangle is a bijection for conformal field theories.

Revised on July 26, 2011 18:37:58 by Blake Stacey (76.24.17.38)