# nLab state-field correspondence

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

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