1. R. Haag andD. Kastler:Journ., Math. Phys.,5, 848 (1964).
2. For general sources of information onC *-algebras seeM. A. Neumark:Normierte Algebren, Chap. V, Sect.24 (Berlin, 1959). A brief review concerningC *-algebras can be found also in the Appendix of ref. (1).
3. IfG is the Lorentz group eq. (1) means among others the supposition of the Lorentz invariance of the norm in A. On the other hand the automorphisms representing the Lorentz group have also an additional property (mentioned above). But properly speaking in our considerations we did not use this property as well as the special space-time structure of A.
4. N. Dunford andJ. T. Schwartz Linear Operators I (New York, 1958). For the theory of semigroups of operators see in Chap. VIII.
5. The set of positive elementsA *(+) [{π,a *,a}≥0, for alla∈A] onA * is the set of states. See ref. (1).