Nuclearity and Split for Thermal Quantum Field Theories Dedicated to Prof. Walter Thirring on the occasion of his 70th birthday

We review the heuristic arguments suggesting that any thermal quantum field theory, which can be interpreted as a quantum statistical mechanics of (interacting) relativistic particles, obeys certain restrictions on its number of local degrees of freedom. As in the vacuum representation, these restrictions can be expressed by a ‘nuclearity condition’. If a model satisfies this nuclearity condition, then the net of von Neumann algebras representing the local observables in the thermal representation has the split property.