The Reeh-Schlieder Theorem states that, in the axiomatic formulation of quantum field theory, the vacuum state is cyclic for the algebra of observables localized in any bounded region of spacetime, however small, meaning applying operators drawn only from that small region to the vacuum can approximate any state in the entire Hilbert space. Named for Helmut Reeh and Siegfried Schlieder, it is a striking and much-discussed consequence of locality and the spectrum condition, showing that local field-theoretic observables carry global information about the state.
Facts
StatementThe vacuum state is a cyclic vector for the field algebra corresponding to any open set in Minkowski space. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Reeh-Schlieder theorem (Wikipedia)
Sources
1. Reeh-Schlieder theorem (Wikipedia)
Lead section
The Reeh-Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961.
Lead section, publication note
published by Helmut Reeh and Siegfried Schlieder in 1961
In Branch: Mathematical Physics, Lead paragraph
The Reeh-Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961.
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