# 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.

## 10 Citations

### The Coalescence Approach to Inequivalent Representation: Pre-QM∞ Parallels

- PhilosophyThe British Journal for the Philosophy of Science
- 2021

Ruetsche [2011] argues that the occurrence of unitarily inequivalent representations in quantum theories withinfinitely many degrees of freedom poses a novel interpretational problem. According to…

### The classical limit of a state on the Weyl algebra

- MathematicsJournal of Mathematical Physics
- 2018

This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive…

### Toward an Understanding of Parochial Observables

- PhilosophyThe British Journal for the Philosophy of Science
- 2018

Ruetsche ([2011]) claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This…

### Deduction and definability in infinite statistical systems

- Computer ScienceSynthese
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It is shown that there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the property of finite systems, and the propertiesOf infinite systems contain no information beyond the propertiesof finite systems.

### On Representational Capacities, with an Application to General Relativity

- PhilosophyFoundations of Physics
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Recent work on the hole argument in general relativity by Weatherall (Br J Philos Sci 69(2):329–350, 2018 ) has drawn attention to the neglected concept of (mathematical) models’ representational…

### On Representational Capacities, with an Application to General Relativity

- PhilosophyFoundations of Physics
- 2018

Recent work on the hole argument in general relativity by Weatherall (Br J Philos Sci 69(2):329–350, 2018) has drawn attention to the neglected concept of (mathematical) models’ representational…

### A Complete Bibliography of Publications in Synthese, 2020–2029

- Philosophy

Abduction [336]. Abductive [11, 124]. ability [143]. Absence [188]. absences [233]. absurdity [154]. Acceptable [18]. accepting [120]. account [81, 169, 129, 13, 196, 168]. across [35]. Action [271,…

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This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical…

### The Status of Scaling Limits as Approximations in Quantum Theories

- Philosophy, Physics
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This paper attempts to make sense of a notion of ``approximation on certain scales'' in physical theories. I use this notion to understand the classical limit of ordinary quantum mechanics as a kind…