Unitary inequivalence in classical systems

@article{Feintzeig2015UnitaryII,
  title={Unitary inequivalence in classical systems},
  author={Benjamin H. Feintzeig},
  journal={Synthese},
  year={2015},
  volume={193},
  pages={2685 - 2705}
}
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. 

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