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Interpreting Quantum Theories$
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Laura Ruetsche

Print publication date: 2011

Print ISBN-13: 9780199535408

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199535408.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 18 January 2022

Quantizing

Quantizing

Chapter:
(p.19) 2 Quantizing
Source:
Interpreting Quantum Theories
Author(s):

Laura Ruetsche

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199535408.003.0002

This chapter explicates the Hamiltonian scheme for quantizing classical mechanical theories by finding a Hilbert space representation of the appropriate canonical commutation relations. The chapter also reviews the canonical anticommutation relations, which encapsulate the quantum mechanics of spin systems. Having catalogued reasons to regard unitary equivalence as a robust criterion of physical equivalence for quantum theories obtained by finding representations of the CCRs/CARs, the chapter presents a pair of theorems—the Stone-von Neumann and Jordan-Wigner theorems—that establish that, provided only finitely many degrees of freedom are involved, all representations of the CCRs/CARs for a given quantum theory are unitarily (and so presumptively physically) equivalent.

Keywords:   Hamiltonian quantization, Stone-von Neumann theorem, Jordan-Wigner theorem, unitary equivalence, Hilbert space, quantum theory, canonical commutation relations, Weyl relations, canonical anticommutation relations, physical equivalence

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