A Matter of Degree: Putting Unitary Inequivalence to Work

Abstract

If a classical system has infinitely many degrees of freedom, its Hamiltonian quantization need not be unique up to unitary equivalence. I sketch different approaches (Hilbert space and algebraic) to understanding the content of quantum theories in light of this non-uniqueness, and suggest that neither approach suffices to support explanatory aspirations encountered in the thermodynamic limit of quantum statistical mechanics.