Quantum Mechanics in Nuclear Algebras

S. IGURI; M. CASTAGNINO

Peyresq, Francia

Congreso; II Peyresq Meeting: "Actual Problems in Quantum Mechanics"; 1997

In this talk we will discuss the convenience of using nuclear locally m-convex *-algebras as the mathematical framework for the formulation of quantum principles instead of C*-algebras, which is the usual algebraic approach. While the results of the C*-algebraic theory remain valid, unbounded operators on Hilbert spaces have an abstract counterpart in our formalism. We prove an extremal decomposition theorem, a proper functional representation theorem and an extension of the GNS theorem.