Reeh–Schlieder theorem

The Reeh - Schlieder theorem of quantum field theory is that - in any good approximation - all possible states can be generated by the localized in any space-time region operators from the vacuum. Intuitively, this says that a "particle behind the moon " can be generated by experiments in a laboratory on Earth.

The exact formulation, indicating that the vacuum condition is cyclical and a means of separating for each local algebra observables.

• Cyclically here means that the closure of the set of all states that result from the application of local operators on the vacuum that already has the entire state space.
• A means of separating means here that there is no local operator applied to the vacuum state can result in 0. Specifically, the expected value of all local self-adjoint operator B to form A * A vacuum state in the non-zero.

The Reeh - Schlieder theorem can be derived both from the properties of concrete quantum field theories, as well as from the various axiom systems of QFT.

It is important to emphasize what the Reeh - Schlieder theorem does not say:

• It does not break the micro- causality, observations in space-like areas located do not interfere with each other ( the operators commute ), no cause-and- effect relationship can propagate faster than light.
• The creation of conditions which are located well outside the area under consideration requires exponentially with distance increasing energy. For the generation of an electron in lunar distance as much energy would be necessary that the underground laboratory would turn into a black hole - an indication that the unified, the gravitational comprehensive theory would mitigate the statements of the Reeh - Schlieder theorem.

The theorem was first published in 1961 by Helmut Reeh and Schlieder Siegfried in their work, " Remarks on the Unitäräquivalenz of Lorentz invariant fields ," Nuovo Cimento in.