The Mathematics of Quantum Mechanics: The Partition Analysis

This chapter gives the partitional treatment of quantum measurement along with a number of other applications such as: commuting and non-commuting observables, von Neumann’s two types of quantum processes, the collapse postulate, quantum jumps, Feynman’s rules about adding amplitudes or probabilities (and the resulting “state reduction principle”), the partition version of the principle of identity of indistinguishables, Weyl’s interesting imagery for measurement, and the indistinguishability of like particles. Then the Yoga is used to systematically extend the concepts of ‘classical’ logical entropy to the quantum logical entropy which is then shown to naturally measure the results of quantum measurement. Finally the Yoga is again applied to relate group representations on sets (i.e., a group actions) and group representations on vector spaces over \( \mathbb {C}\) which turn out to have such important applications in particle physics.