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WORLD SCIENTIFIC eBooks

Quantum Indistinguishability: Spin-statistics without Relativity or Field Theory?

Michael Berry, Jonathan M. Robbins

Published Jul 23, 2017• 0 citations
Publisher
DOI
10.1142/9789813221215_0009

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Quantum Indistiguishability: Spin Statistics without Relativity or Field Theory?

Michael Berry, Robbins, JM

•Jan 1, 2000•0 citations

Indistinguishability for quantum particles: spin, statistics and the geometric phase

Michael Berry, Jonathan M. Robbins

WORLD SCIENTIFIC eBooks•Jul 23, 2017•5 citations

Quantum indistinguishability: Spin-statistics without relativity or field theory?

Michael Berry

We review the formulation of quantum mechanics for identical spinning particles with wavefunctions that are singlevalued when permuted configurations are identified. The identification requires the spins to be smoothly permuted along with position variables, so spin is represented in a position-dependent ‘transported basis’, rather than the usual fixed basis. The simplest transported basis, constructed in terms of spins represented as pairs of commuting harmonic oscillators, gives the correct connection between spin and statistics. More complicated constructions can give the wrong exchange sign. The theory is generalized to incorporate additional properties such as isospin, color and strangeness. Some remarks about the relation between this approach and those based on relatitivity and/or field theory are given.

AIP conference proceedings•Jan 1, 2000•9 citations

Non-RQFT Derivations of CPT Invariance and the Spin–Statistics Connection

Jonathan Bain

Chapter 4 evaluates attempts to derive CPT invariance and the spin–statistics connection (SSC) outside the framework of relativistic quantum theories. It first considers attempts at non-relativistic quantum mechanical derivations of the SSC. These attempts split into those that adopt the framework of finite-dimensional (i.e., non-field-theoretic) non-relativistic quantum mechanics, and fall under the general heading of “configuration space approaches,” and an approach that adopts the framework of non-relativistic quantum field theory. The chapter indicates how recent work in the philosophy of physics literature on the relation between permutation invariance and indistinguishability sheds light on the limitations of the former, while the discussion in Chapter 3 demonstrates where the latter fails. The chapter then considers attempts to derive CPT invariance in relativistic classical field theories from both a pragmatist (Lagrangian) and a purist (algebraic) perspective.

Oxford University Press eBooks•Apr 1, 2016•0 citations

Resource Letter SS–1: The Spin-Statistics Connection

Catalina Curceanu, John D. Gillaspy, Robert C. Hilborn

This Resource Letter provides a guide to the literature on the spin-statistics connection and related issues such as the Pauli exclusion principle and particle indistinguishability. Journal articles and books are cited for the following topics: basic resources, general aspects of spin-statistics, the spin-statistics theorem, theories that go beyond the standard spin-statistics theorem, and experimental tests of the spin-statistics theorem and the symmetrization postulate.

American Journal of Physics•Jun 18, 2012•11 citations

Quantum Statistics from Indistinguishability

Andrei Yu. Khrennikov

Springer eBooks•Jan 1, 2023•0 citations
We review the formulation of quantum mechanics for identical spinning particles with wavefunctions that are singlevalued when permuted configurations are identified. The identification requires the spins to be smoothly permuted along with position variables, so spin is represented in a position-dependent ‘transported basis’, rather than the usual fixed basis. The simplest transported basis, constructed in terms of spins represented as pairs of commuting harmonic oscillators, gives the correct connection between spin and statistics. More complicated constructions can give the wrong exchange sign. The theory is generalized to incorporate additional properties such as isospin, color and strangeness. Some remarks about the relation between this approach and those based on relatitivity and/or field theory are given.
Chapter 4 evaluates attempts to derive CPT invariance and the spin–statistics connection (SSC) outside the framework of relativistic quantum theories. It first considers attempts at non-relativistic quantum mechanical derivations of the SSC. These attempts split into those that adopt the framework of finite-dimensional (i.e., non-field-theoretic) non-relativistic quantum mechanics, and fall under the general heading of “configuration space approaches,” and an approach that adopts the framework of non-relativistic quantum field theory. The chapter indicates how recent work in the philosophy of physics literature on the relation between permutation invariance and indistinguishability sheds light on the limitations of the former, while the discussion in Chapter 3 demonstrates where the latter fails. The chapter then considers attempts to derive CPT invariance in relativistic classical field theories from both a pragmatist (Lagrangian) and a purist (algebraic) perspective.