Local nets of unbounded operator algebras

Abstract

Two rigorous mathematical foundations for relativistic quantum field theory are local nets of von Neumann algebras and Wightman field theory. We recall that local nets of von Neumann algebras are local nets of bounded operator algebras, whereas Wightman field theory makes use of unbounded linear operators. In this paper, we introduce local nets of unbounded operator algebras and show how these can be connected with Wightman field theory. This is motivated by the fact that observables in quantum mechanics are unbounded operators in general.