Nuclear maps and modular structures. II. Applications to quantum field theory

Detlev Buchholz, Claudio D'Antoni, Roberto Longo
July 06, 1990
A correspondence between spectral properties of modular operators appearing in quantum field theory and the Hamiltonian is established. It allows to prove the "distal" split property for a wide class of models. Conversely, any model having this property is shown to satisfy the Haag-Swieca compactness criterion. The results lead to a new type of nuclearity condition which can be applied to quantum field on arbitrary space-time manifolds.

modular theory, modular nuclearity, split property