Algebra of physical observables

В. М. Максимов

Jean-Louis Basdevant

Benjamin H. Feintzeig

Ruetsche ([2011]) claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This would signal that in addition to the abstract algebra, one must use Hilbert space representations for some purposes. I argue to the contrary that there is a way to recover all of the physically significant observables by purely algebraic methods. 1. Introduction2. Preliminaries3. Three Extremist Interpretations 3.1. Algebraic imperialism3.2. Hilbert space conservatism3.3. Universalism4. Parochial Observables 4.1. Parochial observables for the imperialist4.2. Parochial observables for the universalist5. Conclusion

M. D. Maia

Edoardo Piparo

This paper is the first of several parts introducing a new powerful algebra: the algebra of the pseudo-observables. This is a C*-algebra whose set is formed by formal expressions involving observables. The algebra is constructed by applying the Occam's razor principle, in order to obtain the minimal description of physical reality. Proceeding in such a manner, every aspect of quantum mechanics acquires a clear physical interpretation or a logical explanation, providing, for instance, in a natural way the reason for the structure of complex algebra and the matrix structure of the formulation of Werner Heisenberg of quantum mechanics. Last but not least, the very general hypotheses assumed, allow one to state that quantum mechanics is the unique minimal description of physical reality.