Operational axioms for C*-algebra representation of transformations

Abstract

It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states. Both notions are crucial for the possibility of performing experiments on the system, in preventing remote instantaneous influences and in allowing calibration of apparatuses. The case of Quantum Mechanics is thoroughly analyzed. The possibility that other no-signaling theories admit a C*-algebra formulation is discussed.

Work presented at the conference {\em Quantum Theory: Reconsideration of Foundations, 4} held on 11-16 June 2007 at the International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences, Vaxjo University, Sweden