Quantum field theory on curved space-times
Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
One of the main results in the algebraic approach to quantum field theory is the so-called Reeh-Schlieder theorem, which asserts that, in the framework of a real scalar field theory on Minkowski space-time, the set of vectors generated from the vacuum by the polynomial algebra of any open region is dense in the underlying Hilbert space. The main goal of the author is to prove that the existence of a state enjoying at least on a suitable region the Reeh-Schlieder property is not restricted to the example of a scalar field theory, but it can be extended to higher spin field theories, most notably the Dirac field, the Proca field and the vector potential. On the other hand, the author proves that the Dirac and the Proca field as well as the vector potential admit even on a generic globally hyperbolic space-time a state which enjoys the Reeh-Schlieder property at least on a suitable open region. To get to this result the author also shows that spin-\(1\) fields can be described as locally covariant quantum field theories regardless of the gauge freedom present in the massless case.
scientific article; zbMATH DE number 6045731
scientific article