# The CPT-theorem in two-dimensional theories of local observables

October 23, 1992

Let $\cal M$ be a von Neumann algebra with cyclic and separating vector $\Omega$, and let $U(a)$ be a continuous unitary representation of $\mathbb R$ with positive generator and $\Omega$ as fixed point. If these unitaries induce for positive arguments endomorphisms of $\cal M$ then the modular group act as dilatations on the group of unitaries. Using this it will be shown that every theory of local observables in two dimensions, which is covariant under translations only, can be imbedded into a theory of local observables covariant under the whole Poincare group. This theory is also covariant under the CPT-transformation.

Keywords:

modular theory, geometric modular action, CPT-theorem, wedge algebras, Borchers triples