The Spin-Statistics Theorem for Anyons and Plektons in d = 2+1

Mund, Jens

doi:10.1007/s00220-008-0628-9

Cited by 21 publications

(24 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Anyons can also be realized without integrating out any statistical gauge fields either as clusters of non-relativistic particles in two spatial dimensions kept together by external one-body potentials, such as a simple harmonic potential, and interacting with each other only via boundary conditions imposed on the multi-body wave functions [15], or as vertex operators in two-dimensional conformal field theories [16]. For a more recent axiomatic treatise without gauge fields, see [17].…”

Section: Jhep02(2014)052mentioning

confidence: 99%

“…The key idea is that at fixed time the configuration space of a collection of massive particles whose trajectories cannot coincide as the result of their interactions has a non-trivial first homotopy group that is represented non-trivially on the multi-body wave-functions or correlation functions involving point-like operators [17]. These representations thus furnish representations of the braid group, which is why Anyon statistics is synonymous to braid statistics.…”

Section: Jhep02(2014)052mentioning

confidence: 99%

See 1 more Smart Citation

Three-dimensional fractional-spin gravity

Boulanger

Sundell

Valenzuela

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ, ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell.

show abstract

Section: Jhep02(2014)052mentioning

confidence: 99%

Section: Jhep02(2014)052mentioning

confidence: 99%

Three-dimensional fractional-spin gravity

Boulanger

Sundell

Valenzuela

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…A different kind of spacelike string-localization arises in d = 1 + 2 Wigner representations with anomalous spin [80]. The amazing power of this modular localization approach is that it preempts the spin-statistics connection already in the one-particle setting, namely if s is the spin of the particle (which in d = 1 + 2 may take on any real value) then one finds for the connection of the simplectic complement with the causal complement the generalized duality relation…”

Section: A1 Modular Localization Of Statesmentioning

confidence: 99%

“…where the square of the twist operator Z = e πis is easily seen (by the connection of Wigner representation theory with the two-point function) to lead to the statistics phase: Z 2 = statistics phase [80]. The one-particle modular theory also leads to a relation which may be considered as the proto-form of crossing in the one-particle space 1 2 jψ(p) =ψ(−p) (41) in words the 1 2 j = s * transformed wave function is equal to the complex conjugate (antiparticle) of the analytically continued (from forward to backward mass shell) wave function.…”

Section: A1 Modular Localization Of Statesmentioning

confidence: 99%

A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

Schroer

2010

Found Phys

View full text Add to dashboard Cite

The crossing property is perhaps the most subtle aspect of the particlefield relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization-and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from "modular localization" including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where "dynamic" means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4, 2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d = 9 + 1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. Dedicated to Ivan Todorov on the occasion of his 75th birthday. B. Schroer ( ) CBPF, Rua Dr. Xavier Sigaud 150,

show abstract

“…The corresponding particles are called Plektons, or Anyons [105] in the Abelian case, and have fractional spin. In [103] an extended version of the spin statistics theorem in three dimensions was found and in [106] it is shown under more general assumptions that the hypothesis…”

Section: Projection Of Quantum Fields and Statisticsmentioning

confidence: 99%

Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow¹

2009

Ann. Phys.

View full text Add to dashboard Cite

We derive a composite fermion model for the fractional quantum Hall effect from relativistic quantum electrodynamics. With simple arguments it is shown that a special Chern Simons transformation of the Dirac electrons in four spacetime dimensions leads in the low energy limit to a single particle Hamiltonian for composite fermions in three dimensions with correction terms such as Rashba-or Dresselhaus-spin-orbit coupling and zitterbewegung. Furthermore we provide a mechanism to quantum-mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions. This leads to a relativistic field theory and especially a composite fermion field theory in three dimension. This projection map can be combined with the projection onto a Landau level or composite fermion Landau level respectively. This results in a quasi relativistic quantum field theory on a noncommutative plane. The phenomenological models resulting from this approach are discussed and allow a systematical exploration of the effects of the spin and the condensation in a Landau level. We expect from the relativistic approach corrections in terms of spin-orbit coupling effects. From the projection onto Landau levels we expect a modification of the dispersion relation and a modified composite fermion mass. Furthermore, the BRST quantization for Chern Simons theories with compact gauge group is reviewed and the phenomenological consequences within a composite fermion model with spin are discussed. The connection to Wess Zumino Witten theories is recalled and a possible link between the corresponding central charge of the related affine Lie algebra and the composite fermion filling factor is pointed out.

show abstract

The Spin-Statistics Theorem for Anyons and Plektons in d = 2+1

Cited by 21 publications

References 19 publications

Three-dimensional fractional-spin gravity

Three-dimensional fractional-spin gravity

A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

Quantum field theory and composite fermions in the fractional quantum Hall effect

Contact Info

Product

Resources

About