Fermion to boson mapping

The enveloping algebra, D_n, of fermions is extended on the lattice to include the discrete space invariance. This extended algebra, denoted X, has the space symmetry as a factor: X/D_n = space group.     

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama’s program. A novel field strength G = ∂F + fAF arises besides the one of the first order treatment, F = ∂A − ∂A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L_P ∝ G². In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov’s Lagrangian.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer-Julia-Scherk supergravity becomes manifest when its three-form field A₃ is expressed through a set of one-form gauge fields, , , η_1α, and E^a, ψ^α. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A₃ extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E^(11|32) cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A₃ field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A₃. The extra gauge symmetries are also present in the so-called rheonomic treatment of the first order D = 11 supergravity action when A₃ is composite. Our considerations on the composite structure of A₃ provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace .     

Adjoint QCD1 + 1 in light-cone gauge, quantized at equal time

SU (2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with “twisted” boundary conditions, periodic for one color component (the diagonal 3-component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.     

Synthesis, microstructure and photoluminescence of Eu/Tb activated Y2SiO5 nanophosphors by new silicate sources

Y_2−xTb_xSiO₅ and Y_2−xEu_xSiO₅ nanophosphors with seven different kinds of silicate sources were synthesized by sol-gel method. The structures have been investigated to be composed of nanometer-size grains of 30-60 nm through X-ray diffraction (XRD) and scanning electron microscopy (SEM) was used to compare the different morphology of patterns from seven different silicon sources. The photoluminescence of Y_2−xTb_xSiO₅ was investigated as a function of silicate sources and the results revealed that these nanometer materials showed the characteristic emission ⁵D₄ → ⁷F_J (J = 6, 5, 4, 3) of Tb ions. The characteristic emission ⁵D₀ → ⁷F_J (J = 1, 2, 4) of Eu ions was also found in the materials of Y_2−xEu_xSiO₅.     

EPR theoretical study of local lattice structure in ZnS:Cr system

By analyzing the EPR parameters a, D and F of Cr²⁺ ion located at tetrahedral site in ZnS, the local structure around Cr²⁺ in the crystal has been investigated on the basis of the complete energy matrix for a d⁴ configuration in a tetragonal ligand-field within a strong-field-representation. It is shown that there exists an expansion distortion in the local lattice structure. From EPR calculation, the distortion parameters ΔR=0.13 Å and Δθ=1.417° are determined.     

Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes

We develop two theoretical approaches for dealing with the low-energy effects of the repulsive interaction in one-dimensional electron systems. Renormalization Group methods allow us to study the low-energy behavior of the unscreened interaction between currents of well-defined chirality in a strictly one-dimensional electron system. A dimensional regularization approach is useful, when dealing with the low-energy effects of the long-range Coulomb interaction. This method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1. We can also compare these approaches with the Luttinger model, to analyze the effects of the short-range term in the interaction. Thanks to these methods, we are able to discuss the effects of a strong magnetic field B in quasi one-dimensional electron systems, by focusing our attention on Carbon Nanotubes. Our results imply a variation with B in the value of the critical exponent α for the tunneling density of states, which is in fair agreement with that observed in a recent transport experiment involving carbon nanotubes. The dimensional regularization allows us to predict the disappearance of the Luttinger liquid, when the magnetic field increases, with the formation of a chiral liquid with α = 0.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

Dielectric properties of SrBi2−xPrxNb2O9 ceramics (x=0, 0.04 and 0.2)

SrBi_2−xPr_xNb₂O₉ (x=0, 0.04 and 0.2) ceramics were prepared by a solid state reaction method. X-ray diffraction analysis indicated that single-phase layered perovskite structure ferroelectrics were obtained. A relaxor behavior of frequency dispersion was observed among Pr-doped SrBi₂Nb₂O₉. The degree of frequency dispersion ΔT increased from 0 for x=0-7 °C for x=0.2, and the extent of relaxor behavior γ increased from 0.94 for x=0-1.45 for x=0.2. The substitution of Pr ions for Bi³⁺ ions in the Bi₂O₂ layers resulted in a shift of the Curie point to lower temperatures and a decrease in remanent polarization. In addition, the coercive field 2E_c reduced from 110 kV/cm for an undoped specimen to 90 kV/cm for x=0.2.     

Synthesis and luminescence investigation of RE (Eu, Tb and Ce)-doped lithium silicate (Li2SiO3)

Synthesis and photoluminescence (PL) investigations of lithium metasilicate doped with Eu³⁺, Tb³⁺ and Ce³⁺ were carried out. PL spectra of Eu-doped sample showed peaks corresponding to the ⁵D₀→⁷F_j (j=1, 2, 3 and 4) transitions under ultraviolet excitation. Strong red emission coming from the hypersensitive ⁵D₀→⁷F₂ transition of Eu³⁺ ion suggested the presence of the dopant ion in structurally disordered environment. Tb³⁺-doped silicate sample showed blue-green emission corresponding to the ⁵D₄→⁷F_j (j=6, 5 and 4) transitions. Ce-doped sample under excitation from UV, showed a broad emission band in the region 350-370 nm with shoulders around 410 nm. The fluorescence lifetimes of Eu³⁺ and Tb³⁺ ions were found out to be 790 and 600 μs, respectively. For Ce³⁺, the lifetime was of the order of 45 ns. PL spectra of the europium- and terbium-doped samples were compared with commercial red (Y₂O₃:Eu³⁺) and green (LaPO₄:Tb³⁺) phosphors, respectively. It was found that the emission from the doped silicate sample was 37% of the commercial phosphor in case of the Tb-doped sample and 8% of the commercial phosphor in case of the Eu-doped sample.     

Energy transfer and upconversion luminescence in Tm/Yb co-doped lanthanum-zinc-lead-tellurite glasses

A series of Tm³⁺/Yb³⁺ co-doped lanthanum-zinc-lead-tellurite (TPZL) glasses pumped by a 980 nm laser diode (LD) were demonstrated to obtain a high efficiency of infrared-to-visible upconversion. Effects of PbO content on the thermal stability, structure and upconversion properties of Tm³⁺/Yb³⁺ co-doped TPZL glasses had been investigated. The efficient visible upconversion fluorescences corresponding to the ¹G₄→³H₆, ¹G₄→³F₄ and ³H₄→³H₆ transitions of Tm³⁺ were observed under 980 nm excitation. The upconversion intensities of blue, red and near infrared emissions in Tm³⁺/Yb³⁺ co-doped TPZL glasses were obviously enhanced with increasing PbO content. The dependence of upconversion intensities on excitation power and the possible upconversion mechanisms had been evaluated by a proper rate equation model. Population density in different levels and coefficients of the energy transfer rate C_Di (i=2, 4, 6) between Tm³⁺ and Yb³⁺ were estimated by fitting the simulated curves to the measured ones. The obtained three energy transfer coefficients C_D2, C_D4, and C_D6 were determined to be 5.7×10⁻¹⁷, 1.3×10⁻¹⁶ and 8.6×10⁻¹⁷ cm³/s, respectively.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

Anyonic order parameters for discrete gauge theories on the lattice

We present a new family of gauge invariant non-local order parameters for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular, cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the ’t Hooft operators, respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.     

Lorentz anomaly in arbitrary dimensions

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelian gauge fields do in even dimensions larger than or equal to six. The anomaly is proportional toD/2–1 power to the charge, whereD is a number of space-time dimensions.     

Matter fields in lattice gravity

The formulations of the scalar, spinor and gauge fields on a curved random lattice are discussed. A new fermion scheme — simplicial fermions — which is more natural in the presence of gravity, is introduced. Some of the propagators in D = 2 are evaluated numerically and are compared with the continuum limit.     

Low temperature specific heat of bi-layered manganites La2−2xSr1+2xMn2O7 (x=0.3 and 0.5)

The specific heat (C) of bi-layered manganites La_2−2xSr_1+2xMn₂O₇ (x=0.3 and 0.5) is investigated for the ground state of low temperature excitations. A T^3/2 dependent term in the low temperature specific heat (LTSH) is identified at zero magnetic field and suppressed by magnetic fields for x=0.3 sample, which is consistent with a ferromagnetic metallic ground state. For x=0.5 sample, a T² term is observed and is consistent with a two-dimensional (2D) antiferromagnetic insulator. However, it is almost independent of magnetic field within the range of measured temperature (0.6-10 K) and magnetic field (6 T).