The Connection Between Spin and Statistics

Pauli, Wolfgang

doi:10.1103/physrev.58.716

Cited by 638 publications

(397 citation statements)

References 6 publications

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“…The causality is usually addressed as a quantum feature that requires the commutation between observables separated by a space-like interval, which one calls microcausality in field theory [9]. In this section, however, one analyzes causality under a classical tree-level perspective, in which it is related to the positivity of a usual Lorentz invariant, k 2 .…”

Section: Dispersion Relations Stability and Causality Analysismentioning

confidence: 99%

Erratum: Dimensional reduction of a Lorentz- andCPT-violating Maxwell-Chern-Simons model [Phys. Rev. D67, 125011 (2003)]

Belich¹,

Ferreira²,

Helayël-Neto³

et al. 2004

Phys. Rev. D

108

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Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional reduction to D = 1 + 2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, v µ . In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of v µ . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitarity of the gauge sector is assured without any restriction, while the scalar sector is unitary only in the space-like case.

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Section: Dispersion Relations Stability and Causality Analysismentioning

confidence: 99%

Erratum: Dimensional reduction of a Lorentz- andCPT-violating Maxwell-Chern-Simons model [Phys. Rev. D67, 125011 (2003)]

Belich¹,

Ferreira²,

Helayël-Neto³

et al. 2004

Phys. Rev. D

108

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“…These two properties are equivalent by the spin statistics theorem. 46,47 In 2 + 1 dimensions, the requirements of integer spin and trivial statistics are no longer equivalent. There may be particles which have the property that when two of them are fused together, multiple fusion products may arise and the braiding of the original particles is trivial or nontrivial depending on the fusion channel they are in.…”

Section: On Bosonsmentioning

confidence: 99%

Condensate-induced transitions between topologically ordered phases

2009

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We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetrybreaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have noninteger quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories, and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models, and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail.

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“…Thus, the principles of positivity and causality are a priori independent and distinct from the principle of Lorentz symmetry. On the one hand, positivity and causality lead, e.g., to the spin-statistics theorem [53,54], which is a cornerstone of quantum field theory. On the other hand, polynomial Lorentz-violating dispersion relations fail to satisfy these requirements above scales associated with the underlying theory [11].…”

Section: Positivity and Causalitymentioning

confidence: 99%