Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Spin-cluster effects and frustration in the uniaxial spin glass Fe2−xTi1+xO5

Transverse-field (TF) muon-spin-relaxation (μSR) and Mössbauer experiments on the uniaxial insulating spin glass Fe_2?xTi_1+xO₅ (x=0.25) have been performed near and below the spin-glass temperature (T _g). The effect of a transverse field on the spin-freezing process and spin-glass state has been investigated by measuring the field-and temperature-dependencies of the μSR parameters. Spin-cluster effects signaled by anomalous μ-spin relaxation have been observed in a temperature region just aboveT _g. An interpretation supported by recently developed theoretical models addressing non-linear relaxation in an intermediate Griffiths phase is offered.     

Construction of Euclidean (QED)2 via lattice gauge theory

Let ν=det_ren(1+K _g ) be the renormalized Matthews-Salam determinant of (QED)₂, where \(K_g = ieA_{g,} S = \left( {\sum {\gamma _\mu \partial } _\mu + m} \right)^{ - 1} \) is euclidean fermion propagator of one of the following boundary conditions: (1) free, (2) periodic at ?Λ, Λ=[?L/2;L/2]², (3) anti-periodic at ?Λ, and \(A_g (x) = (\sum \gamma _\mu A_\mu (x))g(x)\) . Hereg(x)=1 ifxεΛ₀=[?r/2,r/2]² с Λ and 0 otherwise. Then we show

1. νεL ^p (dμ(A)), p>0. Further we prove a new determinant inequality which holds for the QED, QCD-type models containing fermions. This enables us to prove:
2. Z(Λ₀)=∫νdμ(A)≦exp[c|Λ₀|]. Similar volume dependence is shown for the Schwinger functions.

     

Baryons and baryonium in QCD2

The light particle spectrum of quantum chromodynamics in (1 + 1) dimensions is considered for the limit of strong coupling (g ? m), where g is the coupling constant and m is the bare mass of the fermions. The spectrum is shown to be composed of baryons and baryon-antibaryon bound states. The spectrum is computed to lowest order in m/g and the results are compared with those of other treatments of QCD₂.     

Is the peak value of σ xx at the quantum Hall transition universal?

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σ _xx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σ _xx is reduced by a factor (1 + g/2π)^?1, at least for small g. This provides some theoretical evidence for the non-universality of σ _xx , as observed in a number of experiments.     

Systematic study of horizontal gauge theories

We analyze all the possible continuous horizontal gauge groups G _H in relation with their possibility to explain m _b ? m _t. We assume that the only effective fermionic degrees of freedom correspond to the known fermions but allow the possibility of adding a right handed neutrino to each family. We assume that the Higgs fields which generate masses for these fermions, trough renormalizable Yukawa couplings, transform as an irreducible representation of SU(3)_c ? SU(2)_L ? U(1)_Y ? G_H. Under these assumptions we find two U(1)_H or U(1) _H1 ? U(1) _H2 models free of anomalies and able to guarantee that only the top has a renormalizable mass-generating Yukawa coupling.     

Constraints on non-standard effects from present and futureg μ−2 measurements

Motivated by the expected high accuracy of the next AGS measurement of the muong?2 we have computed several types of contributions arising from new particles and interactions. Results are first given for individual terms where limits on new parameters, coming fromg _μ?2 are compared to those expected from future colliders. Combined effects due to different contributions are then considered and this reveals that constrained models with a low effective scale could still be allowed.     

Supersymmetric electro-weak effects ong μ−2

A model independent analysis of the super-symmetric electroweak contribution tog _μ?2 is discussed within the framework ofN=1 Supergravity unified theory. A detailed comparison with existing experiment of two models (R.G. and T.B.) is carried out. The supersymmetric electro-weak contributions are found to be characteristically different and generally larger than the electro-weak contributions of the standard theory, and in many cases significantly larger. Effects of the hidden sector and the photino mass dependence ofg _μ?2 are also investigated. Present data already eliminates some choices of parameters. Reduction of existing experimental errors by a factor of 3 will make contact with most R.G. models and by a factor of 10 with most T.B. models.     

Unique solution for the weak neutral current coupling constants in purely leptonic interactions

By combining results from the MARK-J at PETRA on Bhabha scattering, μ⁺μ^- and τ⁺τ^- production with recent world data from neutrino-electron scattering experiments, we determine unique values for the leptonic weak neutral current coupling constants g_V and g_A in the framework of electroweak models containing a single Z⁰. In contrast to previous analyses, we only use data from purely leptonic interactions, and therefore avoid the inherent uncertainties resulting from the use of hadronic targets. From the MARK-J data alone in the context of the standard SU(2) ? U (1) model of Glashow, Weinberg and Salam, we find sin²θ_W=0.24±0.11.     

Is every approximate trajectory of some process near an exact trajectory of a nearby process?

This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg _μ for eitherf _μ orF _μ withf _μ (x)=μx forx≦1/2 andf _μ (x)=μ(1?x) forx≧1/2, andF _μ (x)=μx(1?x). For a given μ we will say:g _μ permits increased parameter shadowing if for each δ _x >0 there exists someδ _μ >0 and some δ _f >0 such that every δ _f -pseudog _μ -orbit starting in some invariant interval can be δ _x -shadowed by a realg _α -orbit with α=μ+δ _μ . We show thatg _μ typically permits increased parameter shadowing.     

Orbital quantization in a system of edge Dirac fermions in nanoperforated graphene

The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level E _F, which is varied by the gate voltage V _g, has been studied. Nanoperforation has been performed by irradiating graphene samples on a Si/SiO₂ substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the R(V _g) dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of E _F through an equidistant set of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.     

ESR in the Pd-Mn system: Some evidences of a bottlenecked relaxation for the Mn2+ ion

ESR experiments on Pd-Mn in the low Mn concentration region (200 ? c ? 5000 at. ppm) are reported. The results are consistent with the hypothesis of a bottlenecked resonance with different g-factors for the Mn²⁺ ions (2.055) and the electrons of Pd (2.25); besides, partial opening of this bottleneck can be achieved. A giant momentum for Mn²⁺ (9.15μ_B) is also confirmed.     

Gauge boson/Higgs boson unification: The Higgs bosons as superpartners of massive gauge bosons

The N = 4 supergravity theories with local SO(4) invariance are formulated in superspace. The gauged SO(4) theory with two coupling constants (g₁, g₂) is shown to reduce to three inequivalent models: g₁ = g₂ with negative cosmological constant, g₁ = ?g₂ with positive cosmological constant, and g₁ = 0, g₂ ≠ 0 which is a particular case of the Freedman-Schwarz gauged SU(2) ? SU(2) model. The Higgs effect in the vector-scalar sector of the gauged N = 5 supergravity is analyzed.     

Quarks and leptons

We review the physics of quarks and leptons within the framework of gauge theories for the weak and electromagnetic interactions. The Weinberg-Salam SU(2) × U(1) theory is used as a “reference point” but models based on larger gauge groups, especially SU(2)_L × SU(2)_R × U(1), are discussed. We distinguish among thre “generations” of fundamental fermions: The first generation (e^?, ν_e, u, d), the second generation (μ^?, ν_μ, c, s) and the third generation (τ^?, ν_τ, t, b). For each generation we discuss the classification of all fermions, the charged and neutral weak currents, possible right-handed currents, parity and CP-violation, fermion masses and Cabibbo-like angles and related problems. We review theoretical ideas as well as experimental evidence, emphasizing open theoretical problems and possible experimental tests. The possibility of unifying the weak, electromagnetic and strong interactions in a grand unification scheme is reviewed. The problems and their possible solutions are presented, generation by generation, but a brief subject-index (following the table of contents) enables the interested reader to follow any specific topic throughout the three generations.     

Dark matter from the SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on the SU(4) and SU(2)×SU(2) symmetry groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the fourth generation of fermions are the same as those of the ordinary-matter fermions in the first three generations except for the family charge of the SU(4)_F group: F=(1/3, 1/3, 1/3, ?1), where F=1/3 for fermions of ordinary matter and F=?1 for the fourth-generation fermions. The difference in F does not allow mixing between ordinary and fourth-generation fermions. Because of the conservation of the Fcharge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the fourth generation. As a result, the excess n _B of baryons over antibaryons leads to the excess n_4ν=N?N? of neutrinos over antineutrinos in the fourth generation with n_4ν=n _B . This massive neutrino may form nonbaryonic dark matter. In principle, the mass density of the fourth neutrino n_4νm _N in the Universe can make the main contribution to dark matter, since the lower bound on the neutrino mass m _N from the data on decay of the Z bosons is m _N <m _Z /2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude higher than allowed by observations. This inconsistency may be avoided by nonconservation of the F charge.     

Topological superfluid in one-dimensional ultracold atomic system with spin-orbit coupling

We propose a one-dimensional Hamiltonian H _1D which supports Majorana fermions when d _{x² ? y²}-wave superfluid appears in the ultracold atomic system and obtain the phase diagrams both for the time-reversal-invariant (TRI) case and time-reversal-symmetry-breaking (TRSB) case. From the phase diagrams, we find that the Majorana doublets and the single Majorana fermions exist in the topological superfluid (TSF) regions for the TRI case and the TRSB case, respectively, and we can reach these regions by tuning the chemical potential μ and spin-orbit coupling α _R . Importantly, the spin-orbit coupling has been realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by H _1D is a promising platform to find the mysterious Majorana fermions.     

Experimental constraints on heavy fermions in Higgsless models

Using an effective Lagrangian approach we analyse a generic Higgsless model with composite heavy fermions, transforming as SU(2) _L+R doublets. Assuming that the Standard Model fermions acquire mass through mixing with the new heavy fermions, we constrain the free parameters of the effective Lagrangian studying Flavour Changing Neutral Current processes. In doing so we obtain bounds that can be applied to a wide range of models characterised by the same fermion mixing hypothesis.     

Spontaneous compactification and CPN: SU(3) × SU(2) × U(1), sin2θW, g3/g2 and SU(3)-triplet chiral fermions in four dimensions

We examine the compactification of D=4+2N, Einstein-Maxwell-Dirac theory. It is shown that the manifold CP_N × M₄ is a solution of the equations of motion. The structure of the fermions, gauge bosons and their couplings in the four-dimensional effective theory is investigated. The scale of CP_N is quantized by a generalized Dirac condition. When the results are applied to the solution with internal space CP₁×CP₂, the weak mixing angle and the ratio of the couplings of SU(3) (g₃) and SU(2) (g₂) are defined by two integers and a hypercharge. An SU(3)-triplet chiral fermion can appear in four-dimensional effective theory.     

On the light-by-light contribution to the sixth-order muon anomaly

We have evaluated analytically the coefficient of log m_μ/m_e for the six photon-photon scattering diagrams contributing to the muon g ? 2 in sixth order. The result is remarkably simple, 2π²/3, in complete agreement with the latest numerical evaluation. This completes the analytic calculation of all logarithmic terms in sixth order.     

Application of 2D graded eye-shape scatterers for slow light effect in photonic crystal line defect waveguide

With operating frequency f = 1thz, two-dimensional (2D) graded eye-shape scatterers were firstly applied into photonic crystal waveguide (PCW) for slow light effect in two ways: (1) selecting group index n_g from 31.4 to 95.0, low-dispersion bandwidth (n_g varies within a 10% range) was got from 0.736 μm to 2.334 μm, and ultralow-dispersion bandwidth (n_g varies within a 1% range) was got from 0.438 μm to 0.945 μm by grading the eye-shape scatterers along the longitudinal direction; (2) selecting group index n_g from 32.1 to 98.3, low-dispersion bandwidth was got from 0.559 μm to 1.765 μm, and ultralow-dispersion bandwidth was got from 0.296 μm to 0.661 μm by grading the eye-shape scatterers along the transverse direction. The 2D graded structures can also used in asymmetrical structures and heterostructures for slow light effect.