On the Continuous Extension of States on the Ccr Algebra

The algebra CCR (E) of the CCR depends sensitively on the choice of the one boson test-function space E. Here the unique extension of certain continuous states, resp. representations, to the extended CCR algebra CCR E corresponding to an enlarged test-function space E is studied. Various applications in statistical physics, QED, quantum optics, solid state physics, and quantum chemistry are pointed out.