Unitary inequivalence in classical systems

Benjamin H. Feintzeig

pp. 2685-2705

in: Synthese 193 (9), 2016.

Abstract

Ruetsche (Interpreting quantum theories, 2011) argues that a problem of unitarily inequivalent representations arises in quantum theories with infinitely many degrees of freedom. I provide an algebraic formulation of classical field theories and show that unitarily inequivalent representations arise there as well. I argue that the classical case helps us rule out one possible response to the problem of unitarily inequivalent representations called Hilbert Space Conservatism.