Journal Article

Identical Particles in Quantum Mechanics Revisited

Robert C. Hilborn and Candice L. Yuca

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 53, issue 3, pages 355-389
Published in print September 2002 | ISSN: 0007-0882
Published online September 2002 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/53.3.355
Identical Particles in Quantum Mechanics Revisited

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The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin‐statistics connection and the Symmetrization Postulate. In light of recent theories (such as q‐deformed commutators) that allow for ‘small’ violations of the spin‐statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles.

1 Introduction

2 Philosophical background

2.1 Important terminology

2.1.1 Identity

2.1.2 Indistinguishability

2.1.3 Indiscernibility

2.2 When are particles indistinguishable?

2.3 The Principle of the Identity of Indiscernibles and quantum mechanics

2.4 The Principle of the Identity of Indiscernibles and logic

2.5 Particle history

2.6 Transcendental individuality

3 Some quantum formalism

3.1 The Principle of Permutation Invariance and the Symmetrization Postulate

3.2 The configuration‐space approach

3.3 Commutators and anticommutators, and identical particle statistics

3.4 Q‐mutators

4 Identical particle statistics: a holistic point of view

5 Conclusions

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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