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The British Journal for the Philosophy of Science 2002 53(3):355-389; doi:10.1093/bjps/53.3.355
© 2002 by British Society for the Philosophy of Science
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Identical Particles in Quantum Mechanics Revisited

Robert C. Hilborn1 and Candice L. Yuca2

1 Department of Physics, Amherst College, Amherst, MA 01002, USA. rchilborn{at}amherst.edu 2 Microelectronics Research Centre, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK

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


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