Two-boson truncation of Pauli-Villars-regulated Yukawa theory

We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3 + 1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson-one-fermion equations for eigenstates with J_z = 1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.     

On the renormalization of the bosonized multi-flavor Schwinger model

The phase structure of the bosonized multi-flavor Schwinger model is investigated by means of the differential renormalization group (RG) method. In the limit of small fermion mass the linearized RG flow is sufficient to determine the low-energy behavior of the N  -flavor model, if it has been rotated by a suitable rotation in the internal space. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1$N=1$ or N>1$N>1$, where N   is the number of flavors. For N>1$N>1$ the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1$N=1$ case, where it remains unbroken in the strong coupling phase.     

Electronic structure of GaAs1−xNx under pressure

The electronic band structures of GaAs_1−xN_x for x=0.009, 0.016, 0.031 and 0.062 are calculated ab initio using a supercell approach in connection with the full-potential linear muffin-tin orbital method. Corrections for the ‘LDA gap errors’ are made by adding external potentials which are adjusted to yield correct gaps in pure GaAs. Even small amounts of nitrogen modify significantly the conduction bands, which become strongly non-parabolic. The effective mass in the lowest conduction band thus exhibits strong k-vector dependence. Calculated variations of gaps and effective masses with x and externally applied pressure are presented and compared to a variety of experimental data. There are significant error bars on our results due to the use of the supercell approach. These are estimated by examining the effects of varying the geometrical arrangement of the N-atoms substituting As. However, the calculations show that the electron mass for x>0.009 is much larger than that of pure GaAs, and that it decreases with x.     

Complex-mass renormalization in chiral effective field theory

We consider a low-energy effective field theory of vector mesons and Goldstone bosons using the complex-mass renormalization. As an application we calculate the mass and the width of the ρ meson.     

Enhanced effective mass in doped SrTiO3 and related perovskites

The effective mass is one of the main factors determining the Seebeck coefficient and electrical conductivity of thermo-electrics. In this ab-initio LDA-GGA study the effective mass is estimated from the curvature of electronic bands by one-band-approximation and is in excellent agreement with experimental data of Nb- and La-doped SrTiO₃. It is clarified that the deformation of SrTiO₃ crystals has a significant influence on the bandgap, effective electronic DOS-mass and band-mass, but the electronic effect due to the e_g-band flattening near the Γ-point due to Nb-doping up to 0.2 at% is the main factor for the effective mass increase. Doping of La shows a linear decrease of the effective mass; this can be explained by the different surroundings of A- and B-sites in perovskite. Substitution with other elements such as Ba on the A-site and V on the B-site in SrTiO₃ increases the effective mass as well.     

Contactless electroreflectance of GaNyAs1−y/GaAs multi quantum wells: The conduction band offset and electron effective mass issues

Interband transitions in GaN_yAs_1−y/GaAs multi quantum well (MQW) samples with y=0.012 and 0.023 have been studied by contactless electroreflectance spectroscopy (CER). Optical transitions related to absorption in the GaAs barriers and in the GaN_yAs_1−y/GaAs QWs have been observed and analyzed. The GaAs related transition exhibits clear Franz-Keldysh oscillations with the period corresponding to the built-in electric field of 14 and 17 kV/cm for samples with y=0.012 and 0.023, respectively. The portion of the CER spectrum related to absorption in the GaN_yAs_1−y/GaAs QW exhibits two clear resonances which are attributed to optical transitions between the ground and excited states confined in the QWs. The resonance attributed to the ground state transition is associated with absorption between the first light- and heavy-hole subbands and the first electron subband (11L and 11H) while the resonance attributed to the excited state transition is associated with absorption between the second heavy-hole subband and the second electron subband (22H). The energies of the 11H and 22H transitions have been matched with those obtained from theoretical calculations performed within the effective mass approximation. Thus, the GaN_yAs_1−y/GaAs QWs are type-I structures with a conduction band offset, Q_C, between 70 and 80%. Moreover, the incorporation of N atoms into GaAs is found to cause a significant increase in the electron effective mass. The determined values of electron effective mass for GaN_yAs_1−y/GaAs QW with y=0.012 and 0.023 are 0.105m₀ and 0.115m₀, respectively.     

Photoionization cross-section and binding energy of shallow donor impurities in Ga1−xInxNyAs1−y/GaAs quantum wires

We have investigated the effects of the nitrogen and indium concentrations on the photoionization cross-section and binding energy of shallow donor impurities in Ga_1−xIn_xN_yAs_1−y/GaAs quantum wires. The numerical calculations are performed in the effective mass approximation, using a variational method. We observe that incorporation of small amounts of nitrogen and indium leads to significant changes of the photoionization cross-section and binding energy.     

All about the static fermion bags in the Gross-Neveu model

We review in detail the construction of all stable static fermion bags in the (1+1)-dimensional Gross-Neveu model with N flavors of Dirac fermions, in the large-N limit. In addition to the well known kink and topologically trivial solitons (which correspond, respectively, to the spinor and antisymmetric tensor representations of O(2N)), there are also threshold bound states of a kink and a topologically trivial soliton: the heavier topological solitons (HTS). The mass of any of these newly discovered HTS’s is the sum of masses of its solitonic constituents and it corresponds to the tensor product of their O(2N) representations. Thus, it is marginally stable (at least in the large-N limit). Furthermore, its mass is independent of the distance between the centers of its constituents, which serves as a flat collective coordinate, or a modulus. There are no additional stable static solitons in the Gross-Neveu model. We provide detailed derivation of the profiles, masses, and fermion number contents of these static solitons. For pedagogical clarity, and in order for this paper to be self-contained, we also included detailed appendices on supersymmetric quantum mechanics and on reflectionless potentials in one spatial dimension, which are intimately related with the theory of static fermion bags. In particular, we present a novel simple explicit formula for the diagonal resolvent of a reflectionless Schrödinger operator with an arbitrary number of bound states. In additional appendices we summarize the relevant group representation theoretic facts and also provide a simple calculation of the mass of the kinks.     

Field-theoretical three-body relativistic equations for the multichannel πN↔γN↔ππN↔γπN reactions

A new kind of the relativistic three-body equations for the coupled πN and γN scattering reactions with the ππN and γπN three particle final states are suggested. These equations are derived in the framework of the standard field-theoretical S-matrix approach in the time-ordered three-dimensional form. Therefore, corresponding relativistic covariant equations are three-dimensional from the beginning and the considered formulation is free of the ambiguities which appear due to a three dimensional reduction of the four dimensional Bethe-Salpeter equations. The solutions of the considered equations satisfy the unitarity condition and they are exactly gauge invariant even after the truncation of the multiparticle (n>3) intermediate states. Moreover, the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the construction of the intermediate on shell and off shell Δ resonance states. These intermediate Δ states are obtained after separation of the Δ resonance pole contributions in the intermediate πN Green function. The resulting amplitudes for the Δ⇔Nπ; Δ⇔Nγ; Δ^′⇔Δγ transition have the same structure as the vertex functions for transitions between the on-mass shell particle states with spin 1/2 and 3/2. Therefore it is possible to introduce the real value for the magnetic momenta for the Δ^′⇔Δγ transition amplitudes in the same way as it is done for the N^′⇔Nγ vertex function.     

Monopoles in the presence of the Chern–Simons term via the Julia–Toulouse approach

We study QED₃ with magnetic-like defects using the Julia–Toulouse condensation mechanism (JTM) introduced in [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143, arXiv:hep-th/9604196]. By a careful treatment of the symmetries we suggest a geometrical interpretation for distinct debatable issues in the MCS-monopole system: (i) the induction of the non-conserved electric current together with the Chern–Simons term (CS), (ii) the deconfinement transition and, (iii) the computation of the fermionic determinant in the presence of Dirac string singularities. The JTM leads to proper interpretation of the non-conserved current as originating from Dirac brane symmetry breaking. The mechanism behind this symmetry breaking is clarified. The physical origin of the deconfinement transition becomes evident in the low energy effective theory induced by the JTM. The proper procedure to compute the fermionic determinant in the presence of Dirac branes will be presented. A byproduct of this approach is the possible appearance of statistical transmutation and the clarification for the different quantization rules for the topological mass.     

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x_μx^μ = τ². This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free—a feature characteristic of Dirac’s “point-form” of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincaré generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.     

Quark mass dependence of the pion vector form factor

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ   to pions, g_ρππ$g_{\rho \pi \pi }$, is largely independent of the quark mass while the quark mass dependence of the ρ mass is given by recent lattice data. By employing the Omnès representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the ρππ   coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely 〈r⁴〉=0.73±0.09 fm⁴$〈r^4〉=0.73\pm 0.09{\text{fm}}^4$ or equivalently cV=4.00±0.50 GeV−4$c_V=4.00\pm 0.50{\text{GeV}}^{-4}$.     

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 .     

Nanocrystallite formation in Pd capped PrH3−δ films

Restricting the palladium cap layer thickness to ≤9 nm on top of 170 nm Pr films during in situ hydrogen loading has been shown to result in nanocrystallite size PrH_3−δ films even though the deposited Pr films are of large crystallite size. The effect is attributed to hydrogen-induced stresses in the PrH_3−δ films, which trigger structural rearrangement. These nanocrystalline films show a blue shift of the transmittance edge with respect to PrH_3−δ films of large crystallite size. The approximate size of the nanocrystallites calculated from the blue shift using an effective mass approximation (EMA) theory is supported by XRD, TEM and AFM measurements.     

Interactions for a collection of spin-two fields intermediated by a massless p-form

Under the general hypotheses of locality, smoothness of interactions in the coupling constant, Poincaré invariance, Lorentz covariance, and preservation of the number of derivatives on each field, we investigate the cross-couplings of one or several spin-two fields to a massless p  -form. Two complementary cases arise. The first case is related to the standard interactions from General Relativity, but the second case describes a new, special type of couplings in D=p+2$D=p+2$ spacetime dimensions, which break the PT-invariance. Nevertheless, no consistent, indirect cross-interactions among different gravitons with a positively defined metric in internal space can be constructed.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

The electric field effect on binding energy of hydrogenic impurity in zinc-blende GaN/AlxGa1−xN spherical quantum dot

Within the framework of effective mass approximation, the binding energy of a hydrogenic donor impurity in zinc-blende GaN/Al_xGa_1−xN spherical quantum dot (QD) is investigated using the plane wave basis. The results show that the binding energy is highly dependent on impurity position, QD size, Al content and external field. The binding energy is largest when the donor impurity is located at the centre of the QD and the binding energy of impurity is degenerate for symmetrical positions with respect to the centre of QD without the external electric field. The maximum of the donor binding energy is shifted from the centre of QD and the degenerating energy levels for symmetrical positions with respect to the centre of QD are split in the presence of the external electric field. The binding energy is more sensitive to the external electric field for the larger QD and lower Al content. In addition, the Stark shift of the binding energy is also calculated.