Relativistic non-instantaneous action-at-a-distance interactions

Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The Poincaré invariant parameters that label successive events along the world lines can be identified with the proper times of the particles provided that certain conditions are imposed on the interaction terms in the action. Further conditions on the interaction terms arise from the requirement that mass be a scalar. A generic class of theories with interactions that satisfy these conditions is found. The relativistic equations of motion for these theories are presented. We obtain exact circular orbits solutions of the relativistic one-body problem. The exact relativistic one-body Hamiltonian is also derived. The theory has three components: a linearly rising potential, a Coulomb-like interaction and a dynamical component to the Poincaré invariant mass. At the quantum level we obtain the generalized Klein–Gordon–Fock equation and the Dirac equation.     

Quadrupole and contact interaction of relativistic particles with the electric field of crystals

The Hamiltonian for the quadrupole and the contact interaction of relativistic particles with an electrostatic field is found. The equation of motion for the particle spin is derived.     

A Light-Cone QCD Inspired Effective Hamiltonian Model for Pseudoscalar and Scalar Mesons

Considering the one-gluon exchange interaction and phenomenological quark confinement potential, an improved light-cone effective Hamiltonian for mesons and the corresponding radial mass eigen equations in angular momentum representation is obtained. Solving the J = 0 eigen equations numerically and using a set of adjustable parameters, the obtained solutions for ground states and radial excited states can simultaneously describe both pseudoscalar and scalar flavour-off-diagonal mesons. Some radial excited states are also predicted and wait for experimental test. More results for the vector and axial vector mesons are expected.     

A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions

Starting from the relativistic invariance properties at classical level, we generalize the Darwin equation to the case of non-Coulombic spatial interactions. The relativistic correction terms for vector interactions are derived from a given nonrelativistic potential. We show that, for a Coulombic potential, the results coincide with those obtained in the Coulomb gauge. The results are adapted to the quantum theory obtaining a generalization of the Fermi-Breit equation. An Hermitian interaction operator is constructed. A critical comparison with other possible treatments of the retardation terms is performed also discussing the usual choice of the Coulomb gauge. Special attention is devoted to the construction of a model for quark interaction.     

Wave,particle-family duality and the conservation of discrete symmetries in strong interaction

This paper starts from a nonlinear fermion field equation of motion with a strongly coupled self-interaction. Nonperturbative quark solutions of the equation of motion are constructed in terms of a Reggeized infinite component free spinor field. Such a field carries a family of strongly interacting unstable compounds lying on a Regge locus in the analytically continued quark spin. Such a quark field is naturally confined and also possesses the property of asymptotic freedom. Furthermore, the particular field self-regularizes the interactions and naturally breaks the chiral invariance of the equation of motion. We show why and how the existence of such a strongly coupled solution and its particle-family, wave duality forces a change in the field equation of motion such that it conserves C, P, T, although its individual interaction terms are of V-A and thus C, P nonconserving type.Deceased.     

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.     

Dirac Equation for Scalar,Vector and Tensor Generalized Cornell Interaction

We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.     

Explicit form of the effectiveN-N potential from the quark cluster model

We derive an effectiveN-N potential from a microscopic quark Hamiltonian using the quark cluster model. We construct it in an explicit analytical form, which is expressed only by nuclear variables and which can be used in nuclear structure calculations. To this end we first solve the equation of motion for the six-quark system with a microscopic quark Hamiltonian that includes the quadratic-confinement, one-gluon-, and one-pion-exchange potentials. We then eliminate the quark (internal) degrees of freedom explicitly and express them implicitly in terms of an effectiveN-N potential. The equation of motion for the two-nucleon system is then described by a Schrödinger equation with an effectiveN-N potential. In addition to the one-pion-exchange potential, this effectiveN-N potential contains thequark-exchange potential, which represents the quark-exchange processes associated with a gluon or a pion exchange. This quark-exchange potential is incorporated into the effectiveN-N potential through nonlocal and isospin-dependent terms, which produce a short-range repulsion in theN-N interaction. We give the explicit analytical form of this quark-exchange potential so that it can be used in the nuclear structure calculations.Supported by the DFG under contract number Fa 67/10-5Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

The spin structure of the effective quark Hamiltonian and the hyperfine splittings of charmonium

We provide a simple classical derivation on the spin dependent part of the effective quark Hamiltonian. We suggest that the large S-state hyperfine splitting can be resolved by interpreting that the quark confinement potential is mainly due to an effective scalar exchange.     

Control of electron spin–orbit anisotropy in pyramidal InAs quantum dots

We investigate the electron spin–orbit interaction anisotropy of pyramidal InAs quantum dots using a fully three-dimensional Hamiltonian. The dependence of the spin–orbit interaction strength on the orientation of externally applied in-plane magnetic fields is consistent with recent experiments, and it can be explained from the interplay between Rashba and Dresselhaus spin–orbit terms in dots with asymmetric confinement. Based on this, we propose manipulating the dot composition and height as efficient means for controlling the spin–orbit anisotropy.     

Nucleon magnetic moments in an extended chiral constituent quark model

We present results for the nucleon magnetic moments in the context of an extended chiral constituent quark model based on the mechanism of the Goldstone boson exchange, as suggested by the spontaneous breaking of chiral symmetry in QCD. The electromagnetic charge-current operator is consistently deduced from the model Hamiltonian, which includes all force components for the pseudoscalar, vector and scalar meson exchanges. Thus, the continuity equation is satisfied for each piece of the interaction, avoiding the introduction of any further parameter. A good agreement with experimental values is found. The role of isoscalar two-body operators, not constrained by the continuity equation, is also investigated.     

Theory of the anomalous Hall effect in a semiconductor under uniaxial stress

By including spin orbit dependent contributions, an effective conduction band Hamiltonian for a two band semiconductor is calculated. In doing so we use the band structure of a sample deformed by uniaxial stress. The equations of motion for position and momentum are calculated employing the effective Hamiltonian. With the help of the Boltzmann equation the magnetization-dependent (anomalous) Hall effect is worked out in the case of uniaxial stress on the sample.     

Electric field-induced nonlinear optical properties of a hydrogenic impurity in a GaAs/GaAlAs quantum dot: effects of spin–orbit interactions

Nonlinear optical properties, optical rectification coefficients and the second-order and third-order harmonic generation coefficients as a function of photon energy are dealt in a GaAs/Ga_0.8Al_0.2As quantum dot in the presence of electric field and the spin–orbit interactions. The Dresselhaus and the Rashba spin–orbit interactions are added in the Hamiltonian. The electric field-induced photoionization cross section with the normalized photon energy for an on-centre donor impurity in the quantum dot is studied. The effect of nonparabolicity is included in the Hamiltonian. The spin–orbit interaction as a function of photon energy is investigated. The computations are carried out within the framework of the single band effective mass approximation using variational technique and the compact density approach. It is found that the spin–orbit interaction coefficients show strong effects on the resonant position of harmonic generations. The results are compared with the recent investigations.     

Solutions of the Dirac Equation for the Davidson Potential

In the present paper we solve the Dirac equation with Davidson potential by Nikiforov-Uvarov method. The Dirac Hamiltonian contains a scalar S and a vector V Davidson potentials. With equal scalar and vector potential, analytical solutions for bound states of the corresponding Dirac equations are found.     

Effect of the Quadrupole–Monopole Interaction on Chaos in Compact Binaries

The dynamics of a post‐Newtonian Lagrangian of spinning compact binaries, including the Newtonian, post‐Newtonian, spin‐orbit, spin‐spin, and quadrupole–monopole interaction contributions are investigated herein. According to the Euler–Lagrangian equations, exact and approximate equations of motion can be written. Numerical computations show that the constants of motion can reach satisfactory accuracies in the exact equations but rather poor accuracies in the approximate equations. Similar to the spin–orbit coupling or the spin–spin coupling, the quadrupole–monopole interaction plays a role in some spin effects that lead to the precession of orbits. With the increase in quadrupole–monopole and extension of integration, the orbits precess strongly and the difference in the precession of orbits between the two sets of equations increases. The quadrupole–monopole interaction can also cause the chaoticity of spinning compact binaries. When it increases, chaos is strong under some circumstances in the exact equations but not in the approximate equations.     

A pulse sequence for averaging the strong homonuclear scalar coupling in AB spin systems

A pulse sequence is proposed for the suppression of the strong homonuclear scalar coupling in the case of AB spin systems. The theoretical treatment is presented in terms of the average Hamiltonian theory in the case of aperiodic perturbations. The zero-order and the first-order correction terms in the full average Hamiltonian are calculated. It is shown that the chemical shift interaction for one of the spins is completely refocused and the conditions in which the interactions bilinear in spin operators are efficiently suppressed are analyzed.     

The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in an arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green’s function of the white \(q\bar q\) system over gluon fields, one obtains the relativistic Hamiltonian, which is a matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied using the example of the heavy-light meson and the standard einbein technique is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows good agreement of the results. For an arbitrary \(q\bar q\) system, the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative-energy components is given in conclusion.     

Corrigendum

Theoretical calculations of g-tensor components for the spin–orbit quartet, which arises as the ground state in three-coordinate d⁹ complexes and low-spin d⁷ complexes of D_3h symmetry, have been made on the assumption that the spin–orbit interaction is commensurable with the electron-vibrational interaction. The calculations were carried out within the framework of crystal field theory using representations of the hole formalism. The analytical expressions for g-tensor components were obtained limited to first-order terms. It was shown that the account of the electron–vibrational interaction in the excited quartet only provides three-axial anisotropy for the g-tensor. It was shown that the g-tensor rotates in the plane of the three-coordinate structure with consensual motion of the atoms. The resulting expressions for the g-factor components are in good agreement with experimental data. Being universal for a wide range of contributions of the vibronic and spin–orbit interactions, these expressions essentially fill the gap in studying structures of coordination compounds.     

The mysterious spin-orbit interactions in baryons,non-local forces and thep wave resonances

Within the standard three-quark model of excited baryon resonances we discuss a model which considers one gluon exchange as well as the effects of the confining potential. The latter is assumed universal and scalar but may be non-local (momentum dependent). This leads to an additional type of spin-orbit interactions which can compensate contributions of gluon exchange and explain the general smallness of spin orbit terms. For strange resonances the wave function distortion due to the different quark masses turns out to be very important. The low position of Λ (1405) is a natural consequence in our model.     

Derivation of a Closed Expression of the B-S Interaction Kernel for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter (B-S) equation for quark-antiquark bound states is derived from B-S equations satisfied by the quark-antiquark four-point Green's function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green's function and some other kinds of Green's functions, which follow directly from the QCD generating functional. The derived B-S kernel is given by a closed and explicit expression which contains only a few types of Green's functions. This expression is not only convenient for perturbative calculations, but also applicable for nonperturbative investigations. Since the kernel contains all the interactions taking place in the quark-antiquark bound states, it actually appears to be the most suitable starting point of studying the QCD nonperturbative effect and quark confinement.