A selective history of the Stone-von Neumann theorem

Rosenberg, Jonathan

doi:10.1090/conm/365/06710

Cited by 42 publications

(37 citation statements)

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“…This is a finite group variant of the celebrated Stone-von Neumann Theorem. For a detailed discussion of the history and the various forms of the Stone-von Neumann theorem we refer the reader to [9]. We conclude this section with another immediate corollary of Proposition 11 which tells us that over the field F p every generalized Heisenberg group has the Stone-von Neumann property.…”

Section: Remarkmentioning

confidence: 91%

Maximal representation dimension of finite p-groups

Cernele¹,

Kamgarpour²,

Reichstein³

2011

JGTH

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Section: Remarkmentioning

confidence: 91%

Maximal representation dimension of finite p-groups

Cernele¹,

Kamgarpour²,

Reichstein³

2011

JGTH

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“…The Stone-von Neumann theorem states that all unitary, central representations of the Heisenberg algebra that satisfy (2.21) are equivalent [Ros04].…”

Section: The Heisenberg Algebramentioning

confidence: 99%

The Algebraic Approach to Duality: An Introduction

Sturm

Swart

Völlering

2020

Genealogies of Interacting Particle Systems

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This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise approach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent suggestion by Giardinà, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations of Lie algebras that is crucial for this approach. We also discuss older work by Lloyd and Sudbury on duality functions of product form and the relation between intertwining and duality.MSC 2010. Primary: 82C22, Secondary: 60K35, 17B10, 22E46.

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“…32 For a history of the Stone-von Neumann theorem and an appreciation of its importance, see Rosenberg (2004) . , 1), dx)}, and the deficiency indices are 1, 1 .…”

Section: Quantizationmentioning

confidence: 99%

Essential self-adjointness: implications for determinism and the classical–quantum correspondence

Earman

2008

Synthese

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It is argued that seemingly "merely technical" issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical-quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science.

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A selective history of the Stone-von Neumann theorem

Cited by 42 publications

References 59 publications

Maximal representation dimension of finite p-groups

Maximal representation dimension of finite p-groups

The Algebraic Approach to Duality: An Introduction

Essential self-adjointness: implications for determinism and the classical–quantum correspondence

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