### Citations

304 |
Quantal phase factors accompanying adiabatic changes
- Berry
- 1984
(Show Context)
Citation Context ...relation [5, 6, 7, 8, 9]. Directly from the microscopical wave function (2), by considering the effect of adiabatically rotating quasi-particles around 3 each-other is obtained a Berry phase rotation =-=[10]-=- of ∆γ = 2πν. Directly identifying this rotation with the Aharanov-Bohm phase rotation [12, 11] due to an auxiliary gauge field e∗ ∮ a · dl = 2πe∗Φ/eΦ0, we obtain the solution (for further details see... |

204 |
Topologically Massive Gauge Theories,” Annals Phys
- Deser, Jackiw, et al.
- 1982
(Show Context)
Citation Context ...ched. Similarly to the models describing superconductivity [15, 16, 17] anyons are represented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term =-=[18]-=- for a collective gauge field (interpreted as an effective statistical gauge field) [19, 20, 21, 22]. In these macroscopical models the fractional spin-statistics relation for anyons is set by the val... |

191 |
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
- Laughlin
- 1983
(Show Context)
Citation Context ... of the Hall conductance (1) corresponds to the fractional filling of the lower Landau level of ν3 = 1/3, hence named fractional Hall effect. The Laughlin wave function for the fractional Hall effect =-=[4]-=- was at that time derived phenomenologically and it is the best account for this effect as well as renders very low energies for the wave function solutions. Considering complex coordinates for the fr... |

165 |
On the magnetic properties of superconductors of second group.
- Abrikosov
- 1957
(Show Context)
Citation Context ...n by σijH = e 2/(2k − 1)ǫij from (19) and (20). The remaining of the fractional conductance multiples of these fractions are justified in this model by the existence of finite energy vortex solutions =-=[8, 9, 22, 40, 41, 42]-=- φ = e±iϕ , ai = ±ǫij rj e |r| , (24) here expressed in Cartesian coordinates centred at the origin such that the several Hall conductance (or equivalently the filling fractions) can be obtained by ad... |

134 | SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry,” arXiv:hep-th/0307041
- Witten
(Show Context)
Citation Context ...nsistent with the formulation of the Fractional Quantum Hall Effect in terms of fractional charged anyons, allows for a formulation of these systems in a variational framework of a gauge field theory =-=[53, 54]-=- compatible with the 4-dimensional Maxwell equations [50], hence from more fundamental principles. In the following we are mostly working at semi-classical level with statistical average fields and we... |

127 |
Electronic properties of two-dimensional systems
- Ando, Fowler, et al.
- 1982
(Show Context)
Citation Context ..., not equivalent to each other and only within the framework of pure Chern-Simons theories was possible to show their equivalence [36]. For reviews in the several topics addressed in this section see =-=[39]-=-. 1.3 Landau-Ginzburgh Chern-Simons Models as a Macroscopical Description of the Fractional Hall Effect Next we briefly resume the description of quantum Hall planar systems by effective Chern-Simons ... |

117 |
Quantised Singularities in the Electromagnetic
- Dirac
- 1931
(Show Context)
Citation Context ...ge of the electron, and g is the coupling constant corresponding to the pseudo-photon field C which coincides with the unit of magnetic charge [50] according to the original theory of Dirac monopoles =-=[56]-=-. As for α and β̂ represents the average number of electric and magnetic unit fluxes carried by each anyon in the system; 2. φ∗φ is real and transforms as a scalar under the discrete symmetries P and ... |

101 |
Concept of Non-Integrable Phase Factors and Global Formulations of Gauge Fields, Phys
- Wu, Yang
- 1975
(Show Context)
Citation Context ...s our original assumptions when setting up the model. In the next section we discuss the relation between the unit electric charge e and unit magnetic charge g assuming Dirac’s quantization condition =-=[56, 57]-=- and showing that, for the model derived here, it is equivalent to the quantization of magnetic flux [58]. 2.3 The Fractional Hall Conductance, Dirac’s Quantization Condition and Quantization of Magne... |

84 |
New Method for High-Accuracy Determination of the Fine-Structure
- Klitzing, Dorda, et al.
- 1980
(Show Context)
Citation Context ...al and 3-dimensional Lorentz discrete symmetries P , T and C. 1.1 Quantum Hall Effect and Fractional Statistics The integer Hall effect was first analyzed experimentally by Klitzing, Dorda and Pepper =-=[1]-=- in 1980 and explained theoretically by Laughlin [2]. For high mobility planar electron systems at low temperature under an orthogonal (to the planar system) strong magnetic field B, when a longitudin... |

83 |
Fractional quantization of the Hall effect: A hierarchy of incompressible quantum fluid states
- Haldane
- 1983
(Show Context)
Citation Context ... fluid (or OCP plasma). Soon it was derived that these quasi-holes and quasi-particles do not obey either a Fermi or a Bose spinstatistics relation, instead have a fractional spin-statistics relation =-=[5, 6, 7, 8, 9]-=-. Directly from the microscopical wave function (2), by considering the effect of adiabatically rotating quasi-particles around 3 each-other is obtained a Berry phase rotation [10] of ∆γ = 2πν. Direct... |

72 |
the quantum adiabatic theorem, and Berry’s phase, Phys
- Simon, Holonomy
- 1983
(Show Context)
Citation Context ... the effect of adiabatically rotating quasi-particles around 3 each-other is obtained a Berry phase rotation [10] of ∆γ = 2πν. Directly identifying this rotation with the Aharanov-Bohm phase rotation =-=[12, 11]-=- due to an auxiliary gauge field e∗ ∮ a · dl = 2πe∗Φ/eΦ0, we obtain the solution (for further details see the original work of Arovas, Schrieffer and Wilczek [8] and references therein) e∗ ∮ a · dl = ... |

67 |
Bound Electron Pairs in a Degenerate Fermi Gas,” Phys.
- Cooper
- 1956
(Show Context)
Citation Context ...anyons are commonly considered as spin 0 bosons[14] interpreted as composite fermions constituted by one electron with magnetic vortexes attached. Similarly to the models describing superconductivity =-=[15, 16, 17]-=- anyons are represented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term [18] for a collective gauge field (interpreted as an effective statisti... |

57 |
Quantum mechanics of fractional-spin particles, Phys
- Wilczek
- 1982
(Show Context)
Citation Context ... fluid (or OCP plasma). Soon it was derived that these quasi-holes and quasi-particles do not obey either a Fermi or a Bose spinstatistics relation, instead have a fractional spin-statistics relation =-=[5, 6, 7, 8, 9]-=-. Directly from the microscopical wave function (2), by considering the effect of adiabatically rotating quasi-particles around 3 each-other is obtained a Berry phase rotation [10] of ∆γ = 2πν. Direct... |

46 |
Composite-fermion approach for the fractional quantum Hall effect
- Jain
- 1989
(Show Context)
Citation Context ...sented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term [18] for a collective gauge field (interpreted as an effective statistical gauge field) =-=[19, 20, 21, 22]-=-. In these macroscopical models the fractional spin-statistics relation for anyons is set by the value of the Chern-Simons coupling. Purely at macroscopical model level this choice is imposed external... |

45 |
Microscopic Theory of Superconductivity, Phys
- Bardeen, Cooper, et al.
- 1957
(Show Context)
Citation Context ...anyons are commonly considered as spin 0 bosons[14] interpreted as composite fermions constituted by one electron with magnetic vortexes attached. Similarly to the models describing superconductivity =-=[15, 16, 17]-=- anyons are represented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term [18] for a collective gauge field (interpreted as an effective statisti... |

43 | The Partition Function Of A Degenerate Functional - Schwarz - 1979 |

42 |
On the theory of superconductivity. Zh
- Ginzburg, Landau
- 1950
(Show Context)
Citation Context ...anyons are commonly considered as spin 0 bosons[14] interpreted as composite fermions constituted by one electron with magnetic vortexes attached. Similarly to the models describing superconductivity =-=[15, 16, 17]-=- anyons are represented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term [18] for a collective gauge field (interpreted as an effective statisti... |

39 |
Quantized Hall conductivity in two dimensions, Phys
- Laughlin
- 1981
(Show Context)
Citation Context ... T and C. 1.1 Quantum Hall Effect and Fractional Statistics The integer Hall effect was first analyzed experimentally by Klitzing, Dorda and Pepper [1] in 1980 and explained theoretically by Laughlin =-=[2]-=-. For high mobility planar electron systems at low temperature under an orthogonal (to the planar system) strong magnetic field B, when a longitudinal (along the direction of the planar system) electr... |

22 |
Large scale physics of the quantum Hall fluid
- Frohlich, Zee
- 1991
(Show Context)
Citation Context ...harge has always numerator 1 and an odd integer denominator. Prior to these developments have been also considered effective theories with pure gauge Chern-Simons theories having several gauge fields =-=[34, 35, 36, 37, 38]-=- corresponding to a gauge symmetry group U(1)N . These theories are interpreted as an effective description of the Hall effect containing only gauge degrees of freedom (the anyon field is integrated o... |

22 |
Vortex-line models for Dual Strings”, Nucl. Phys. B61
- Nielsen, Olesen
- 1973
(Show Context)
Citation Context ...n by σijH = e 2/(2k − 1)ǫij from (19) and (20). The remaining of the fractional conductance multiples of these fractions are justified in this model by the existence of finite energy vortex solutions =-=[8, 9, 22, 40, 41, 42]-=- φ = e±iϕ , ai = ±ǫij rj e |r| , (24) here expressed in Cartesian coordinates centred at the origin such that the several Hall conductance (or equivalently the filling fractions) can be obtained by ad... |

14 |
Fermi-Bose Transmutation Induced by Gauge
- Polyakov
- 1988
(Show Context)
Citation Context ...rum as has been derived for example in [26] (for 3 + 1-dimensions). Also considering several charge insertions constraint the allowed charge spectrum of the theory due to the braiding of Wilson lines =-=[27]-=-. Chern-Simons and Maxwell Chern-Simons have been often used as a gauge description of conformal field theories[28], as for example string theory [29, 30, 31, 32, 33]. In all these frameworks the valu... |

13 |
Canonical Quantum Field Theory with Exotic Statistics,” Phys.Rev.Lett
- Semenoff
- 1988
(Show Context)
Citation Context ...fractional spin-statistics relation for anyons is set by the value of the Chern-Simons coupling. Purely at macroscopical model level this choice is imposed externally not being derived from the model =-=[24, 25, 23]-=-, the Abelian Chern-Simons coupling is, generally, a free parameter. It is important to stress that in the original derivation of Chern-Simons models from the microscopical description the value of th... |

13 |
Effective theories of the fractional quantum Hall effect at generic filling fractions
- Blok, Wen
- 1990
(Show Context)
Citation Context ...harge has always numerator 1 and an odd integer denominator. Prior to these developments have been also considered effective theories with pure gauge Chern-Simons theories having several gauge fields =-=[34, 35, 36, 37, 38]-=- corresponding to a gauge symmetry group U(1)N . These theories are interpreted as an effective description of the Hall effect containing only gauge degrees of freedom (the anyon field is integrated o... |

12 | Order Parameter and Ginzburg-Landau Theory for the Fractional Quantum Hall Effect - Read - 1989 |

10 | Explicit Actions for Electromagnetism with Two Gauge Fields with Only one Electric and one Magnetic Physical
- Ferreira
(Show Context)
Citation Context ...46] for a similar construction), in the following we give another solution to this problem by considering the internal gauge field to be a pseudo-vector which naturally arises in pseudo-photon theory =-=[47, 49, 50, 48, 51, 52]-=-. Concerning the second point we note that it is today an experimental fact that in fractional Hall systems anyons have fractional charge as has been verified by several independent groups [45]. At mo... |

9 |
Quantum Electrodynamics with Dirac Monopoles, Nuovo Cimento 23
- Cabibbo, Ferrari
- 1962
(Show Context)
Citation Context ...46] for a similar construction), in the following we give another solution to this problem by considering the internal gauge field to be a pseudo-vector which naturally arises in pseudo-photon theory =-=[47, 49, 50, 48, 51, 52]-=-. Concerning the second point we note that it is today an experimental fact that in fractional Hall systems anyons have fractional charge as has been verified by several independent groups [45]. At mo... |

8 |
The off-shell closed strings as topological open membranes. Dynamical transmutation of world sheet dimension
- Kogan
- 1989
(Show Context)
Citation Context ...of the theory due to the braiding of Wilson lines [27]. Chern-Simons and Maxwell Chern-Simons have been often used as a gauge description of conformal field theories[28], as for example string theory =-=[29, 30, 31, 32, 33]-=-. In all these frameworks the value of the Abelian Chern-Simons coupling is fixed externally depending on the physical system that we are describing. 1.2 Generic Filling Fractions νn,m = n/m So far we... |

8 |
Universality in quantum Hall systems,” Nucl. Phys. B354
- Frohlich, Kerler
- 1991
(Show Context)
Citation Context ...harge has always numerator 1 and an odd integer denominator. Prior to these developments have been also considered effective theories with pure gauge Chern-Simons theories having several gauge fields =-=[34, 35, 36, 37, 38]-=- corresponding to a gauge symmetry group U(1)N . These theories are interpreted as an effective description of the Hall effect containing only gauge degrees of freedom (the anyon field is integrated o... |

8 |
Electromagnetism with Magnetic Charge and Two Photons
- Singleton
- 1996
(Show Context)
Citation Context ...46] for a similar construction), in the following we give another solution to this problem by considering the internal gauge field to be a pseudo-vector which naturally arises in pseudo-photon theory =-=[47, 49, 50, 48, 51, 52]-=-. Concerning the second point we note that it is today an experimental fact that in fractional Hall systems anyons have fractional charge as has been verified by several independent groups [45]. At mo... |

7 |
Taming the conformal Zoo, Phys. Lett. B220
- Moore, Seiberg
- 1989
(Show Context)
Citation Context ...traint the allowed charge spectrum of the theory due to the braiding of Wilson lines [27]. Chern-Simons and Maxwell Chern-Simons have been often used as a gauge description of conformal field theories=-=[28]-=-, as for example string theory [29, 30, 31, 32, 33]. In all these frameworks the value of the Abelian Chern-Simons coupling is fixed externally depending on the physical system that we are describing.... |

6 | Open and unoriented strings from topological membrane - I. prolegomena, J.High Energy Phys. 0106
- Ferreira, Kogan
- 2001
(Show Context)
Citation Context ...rrespond to the inversion of one of the axis (the inversion of both x and y is equivalent to a planar rotation). Hence we choose to invert the y coordinate such that P(3D) and T(3D) 32 are defined as =-=[32]-=-: P(3D) : y → −y T(3D) : t → −t A0 → +A0 A0 → −A0 Ax → +Ax Ai → +Ai Ay → −Ay C0 → −C0 C0 → +C0 Cx → −Cx Ci → −Ci Cy → +Cy Ex(3D) → +Ex(3D) Ei(3D) → +Ei(3D) Ey(3D) → −Ey(3D) Ẽ(3D) → +Ẽ(3D) Ẽ(3D) → +... |

6 |
Superconducting ground state of noninteracting particles obeying fractional statistics
- Laughlin
(Show Context)
Citation Context ...considered that the anyons have unit electric charge e∗ = e such that α = 1 and the integer filling fraction ν1,1/p = p corresponds for each p electrons to have, in average, one unit of magnetic flux =-=[44, 8, 43, 22]-=- such that |β| = 1/p. By considering further 2q flux tubes attached to each electron (an even integer is necessary due to the induced phase change [22, 8]) we obtain the full Jain Hierarchy of fractio... |

5 |
Chiral spin states and superconductivity Phys
- Wen, Wilczek, et al.
- 1989
(Show Context)
Citation Context |

5 |
Ein neuer effect bei eintritt der supraleitfähigkeit
- Meissner, Ochsenfeld
- 1933
(Show Context)
Citation Context ... unit electric charge e and unit magnetic charge g assuming Dirac’s quantization condition [56, 57] and showing that, for the model derived here, it is equivalent to the quantization of magnetic flux =-=[58]-=-. 2.3 The Fractional Hall Conductance, Dirac’s Quantization Condition and Quantization of Magnetic Flux So far we have not explicitly specified the relation between the unit electric charge e and the ... |

4 |
Open Strings From Three-Dimensions: Chern-Simons-Witten Theory On Orbifolds
- Hořava
- 1996
(Show Context)
Citation Context ...of the theory due to the braiding of Wilson lines [27]. Chern-Simons and Maxwell Chern-Simons have been often used as a gauge description of conformal field theories[28], as for example string theory =-=[29, 30, 31, 32, 33]-=-. In all these frameworks the value of the Abelian Chern-Simons coupling is fixed externally depending on the physical system that we are describing. 1.2 Generic Filling Fractions νn,m = n/m So far we... |

4 | A Pseudo-Photon in Non-Trivial Background - Ferreira |

4 | Ue(1) × Ug(1) actions in 2+1-dimensions: Full vectorial electric and magnetic
- Ferreira
(Show Context)
Citation Context |

3 |
Effective-Field-Theory for the Fractional Quantum
- Zhang, Hansson, et al.
- 1989
(Show Context)
Citation Context ...sented by a scalar complex field φ. For the Fractional Hall effect it is further considered a Chern-Simons term [18] for a collective gauge field (interpreted as an effective statistical gauge field) =-=[19, 20, 21, 22]-=-. In these macroscopical models the fractional spin-statistics relation for anyons is set by the value of the Chern-Simons coupling. Purely at macroscopical model level this choice is imposed external... |

3 |
Gauging Dual Symmetry
- Kato, Singleton
- 2002
(Show Context)
Citation Context ...or σijH should transform as a tensor instead of transforming as a pseudo-tensor. The most straight forward solution is to consider the Chern-Simons coupling θk to be a pseudo-scalar (see for instance =-=[46]-=- for a similar construction), in the following we give another solution to this problem by considering the internal gauge field to be a pseudo-vector which naturally arises in pseudo-photon theory [47... |

3 |
Classical Electrodynamics. Wiley, third edition,
- Jackson
- 1998
(Show Context)
Citation Context ...everses the time coordinate direction t. The several vector and pseudovector fields and currents and scalar and pseudo-scalar charge densities are mapped according to the 30 following transformations =-=[50, 60]-=-: P(4D) : x i → −xi T(4D) : t → −t A0 → +A0 A0 → −A0 Ai → −Ai Ai → +Ai C0 → −C0 C0 → +C0 Ci → +Ci Ci → −Ci Ei(4D) → −Ei(4D) Ei(4D) → +Ei(4D) Bi(4D) → +Bi(4D) Bi(4D) → −Bi(4D) ρe(4D) → +ρe(4D) ρe(4D) →... |

3 |
Fractional quantum Hall effect in a two-dimensional electronhole fluid, Phys. Rev. B42
- MacDonald, Rezayi
- 1990
(Show Context)
Citation Context ...s create a statistical electric field orthogonal to the system which may be relevant when computing interlayer correlations functions in bi-layer Hall systems having a Bose Einstein Condensate phases =-=[61]-=-. As a preliminary justification for this statement we recall that from a field theory perspective the interactions are due to the gauge fields, for the particular model discussed here the interlayer ... |

3 | The Edge States of the BF System and the London Equations - Balachandran, Teotonio-Sobrinho - 1993 |

2 |
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized
- Alperin
- 1984
(Show Context)
Citation Context ...s of the Hall conductance σH = e/(2Φ0)α/β (or equivalently the Landau filling factors νp,k = α/β = p/(2k − 1)), the model can reproduce either the Jain hierarchy [22] or the Haldane-Alperin hierarchy =-=[6, 7]-=- already discussed in the previous section. However the charge of the quantum excitations will be distinct for each hierarchy as already notice. Let us briefly resume both original hierarchies and its... |

2 |
Quantum Statistics And Superconductivity
- Wen, Zee
- 1990
(Show Context)
Citation Context |

2 |
Foxon, Experimental determination of fractional charge e/q for quasiparticle excitations in the fractional quantum Hall effect, Phys
- Clark, Mallett, et al.
- 1988
(Show Context)
Citation Context ... pseudo-tensor and σijH Ei as a pseudo-vector. 9 2. There is experimental evidence that, for a given Hall conductance σH = e/(2Φ0) p/(2k − 1), the corresponding fractional charges are e∗ = e/(2k − 1) =-=[45]-=-. Therefore interpreting this result in terms of anyons we would expect that the number of magnetic vortexes (number of elementary quantum flux) per electron is 1/p as in Haldane-Alperin Hierarchy whi... |

2 |
Carneiro e M
- Mello, S
(Show Context)
Citation Context |

2 | Canonical Functional Quantization of Pseudo-Photons in Planar Systems, to appear
- Ferreira
(Show Context)
Citation Context ... system, instead the statistical electric and magnetic vortex fluxes will be encoded in the parameters of the model α and β̂, however we note that these fluxes can be described as quantum excitations =-=[55]-=-. Specifically the existence of both kind of vortexes is consistent in 10 the framework of dimensional reduced Ue(1) × Ug(1) extended electromagnetism which we shortly review in the next section. 1.5 ... |

2 | Monopole confinement by flux tube, hep-ph/0605107; Confinement of monopole using flux string - Chatterjee, Lahiri |

2 |
Magnetic Monopoles in Spin Ice, Nature 451 (2008) 42
- Castelnovo, Moessner, et al.
- 2009
(Show Context)
Citation Context ... hence global magnetic charge is null (see also [30] for topological mechanism) or unconfined. We remark that recently macroscopical magnetic monopole configurations have been experimentally observed =-=[64]-=- in Spin Ice systems, hence, similarly, the model configurations with non-null statistical magnetic charge discussed here may represent a field configuration that mimics a magnetic monopole through a ... |

1 | Rotational Anomalies Without Anyons, Phys. Rev. D31 - Hagen - 1985 |