state-field correspondence

A field operator $\varphi $ in a quantum field theory with a distinguished vacuum vector $\mid 0\u27e9$ defines its incoming state as the $\mid {\mathrm{phi}}_{\mathrm{in}}\u27e9:=U(0,-\mathrm{\infty})\varphi \mid 0\u27e9$ i.e. as the limit when time goes to infinity of the state $\varphi \mid 0\u27e9$, 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 ${t}_{2}>{t}_{1}$. The assignment $\varphi \mapsto \mid {\mathrm{phi}}_{\mathrm{in}}\u27e9$ is a bijection for conformal field theories.

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