Where the mathematical structure of Quantum Mechanics coms from
arXiv:quant-ph/0612162
Abstract
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated existence of "faithful states" that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the "adjoint" of a transformation.
Work presented at the conference "Beyond the Quantum" held at the Lorentz Center in Leiden from May 29th through June 2nd 2006. Synthesis of quant-ph/0611094