The Reeh-Schlieder Property for Thermal Field Theories

In this article we will discuss how a strictly local operation can effect a physical system in thermal equilibrium. Let O denote an open and bounded space-time region in Minkowski space IR where a local operation a takes place. The first guess might be that the operation a gives rise to an excitation of the equilibrium state which is localized in O; i.e., with respect to measurements in the causal complement of O the excited state can not be distinguished from the original equilibrium state. Due to the cluster theorem for (extremal) KMS-states this is quantitatively true if a is picked at random in O and measurements at sufficiently large space-like distance are considered. However, we will show that qualitatively the situation is quite different: for any ǫ > 0 and for any normal state ω, one can find an operator aω strictly localized in O which, when applied to the KMS-vector, produces a vector state ω̂ such that ‖ω− ω̂‖ < ǫ. To achieve this the operator aω must exploit the small but non-vanishing long range correlations which exist in an equilibrium state as a consequence of its analyticity properties; the latter simply reflect the basic stability and passivity properties of an equilibrium state.