Gauge covariant linear response analysis of QCD plasma oscillations

We show, using linear response theory, how plasma oscillations and screening in quark-gluon plasma can be computed in perturbation theory in a gauge covariant manner. Using this method we calculate the damping constant of color electric plasma oscillations in a Colomb gauge and show that the result agrees with an earlier calculation in the A₀ = 0 gauge.     

Magnetic moments of spherical nuclei: Status of the problem and unsolved issues

Dipole magnetic moments of more than 100 odd spherical nuclei are calculated within the theory of finite Fermi systems. For the effective interaction of nucleons within the theory of finite Fermi systems, use is made of a version that takes into account nuclear-medium-modified amplitudes for the exchange of one pion and one rho meson. A new tensor local charge ζ _t is incorporated in the theory of finite Fermi systems in addition to the known orbital (ζ _l ) and spin (ζ _s ) local charges. Good agreement with experimental data, at a level of 0.1 to 0.2μ _N , is obtained for the overwhelming majority of the nuclei considered here. Several cases of a significant discrepancy with experimental data, at a level of 0.3 to 0.5μ _N , are revealed. Possibilities for removing these discrepancies are discussed. A detailed comparison with known results obtained within the multiparticle shell model is performed for 2p-to 1f-shell nuclei. Cases where the standard theory of finite Fermi systems must be extended by taking into account multiparticle configurations are found. Magnetic moments are analyzed for a number of long isotopic chains. Several new experimental values of magnetic moments for copper isotopes far from the beta-stability valleys are known. For the example of the copper-isotope chain, it is shown how the emergence of a deformation in the ground state of a nucleus can be revealed on the basis of a systematic analysis of magnetic moments.     

Drag exerted on dislocation kinks in solid solutions

The theory of drag exerted on dislocation kinks by statistical density fluctuations of impurity atoms is generalized to the case of solid solutions. The conditions of the transition to anomalous kink drift, which is characterized by a nonlinear time (t) dependence of the displacement x (x ～ t ^δ, δ < 1), are obtained. The related consequences for the dislocation mobility and the plastic flow of a solid solution are derived. The theory is illustrated through calculating the concentration dependence of the deforming stress in a Ge_1?c Si _c solid solution.     

Subsidiary conditions and physical S-matrix unitarity in indefinite-metric quantum gravitation theory

The quantum theory of gravitational fields is formulated in a manifestly Lorentz covariant manner in the framework of indefinite-metric quantum field theory. The physical state subspace is defined by the two subsidiary conditions Q_B|phys〉 = Q_c|phys〉 = 0, where the conserved charges Q_B and Q_c are the generators of the BRS transformation ond of the Faddeev-Popov ghost scale transformation, respectively. By clarifying the metric structures of the Fock space of asymptotic fields with help of the Ward-Takahashi identities, the physical S-matrix unitarity is established in just the same way as in the canonical theory of Yang-Mills fields.     

Dual-resonance models

Dual-resonance models are treated both as S-matrix theories and as systems of interacting strings. We show how Veneziano was able to construct a dual four-point amplitude with narrow resonances and rising Regge trajectories. The construction is generalized to the N-point amplitude in the manifestly dual manner suggested by Koba and Nielsen. We develop the operator formalism which exhibits the factorization property of the above amplitude. The related questions of ghost elimination and null states are discussed. Models with extra degrees of freedom and, in particular, the Neveu-Schwarz-Ramond model with spin, are treated. The latter model has a quark-line spectrum of mesons, but it possesses massless vector mesons and fermions. It is shown how the operator formalism is related to a quantized string. The theory of such a string is developed, with particular emphasis on the ghost-free “Coulomb-gauge” quantization. By constructing theories of interacting strings, we reproduce the dual-model S-matrix. A brief account is given of the theory of loops, in which one attempts to improve on the narrow-resonance model in a perturbative manner.     

Classical Hamiltonian perturbation theory without secular terms or small denominators

We consider perturbation theory in ? for the classical Hamiltonian H = H₀ + ?H₁, where H₀ gives rise to a known motion and ? is small. First we demonstrate how the usual secular terms and small denominators arise from a straightforward expansion in ? and argue that they are artifacts of the method. Then we present an alternative perturbation theory based on an analysis of the operator (s ? L)^?1, where s is a complex number and L is the Liouville operator corresponding to H. This perturbation series contains neither secular terms nor small denominators. In the case of almost multiply periodic systems we show, to lowest non-trivial order in ?, how our series reproduces the standard results both in the resonant and nonresonant regions — all in one analytic formula. As a final exercise we demonstrate that energy is conserved at order ?ⁿ⁺¹ when the accuracy of the theory is order ?ⁿ.     

Strongly coupled massive QCD3 and frustrated Heisenberg antiferromagnets: fractional statistics and chiral-spin order

Strongly coupled massive SU(N_C) and U(N_C) QCD₃ on a lattice is studied using the 1/N_C expansion. The quark mass terms have a definite sign in the present model, and therefore the system explicitly breaks the parity symmetry. The continuum counterpart generates the Maxwell + Chern-Simons theory by integrating out the quark field. In the present paper, we shall integrate out the gauge fields using the strong-coupling expansion and obtain a frustrated quantum Heisenberg model as an effective model. The ground state of the above effective quantum spin model is studied using the large-N_C approximation. There are two phases; one is a Neel-ordered state and the other is a state with a chiral-spin order. It is explicitly shown that the chiral-spin ordered state corresponds to a state with spontaneous generation of color magnetic flux in the original theory and fractional statistics appears in that phase. This result strongly suggests that there are (at least) two phases in the massive QCD₃ and Maxwell-CS theory. One is the confinement phase and the other is the perturbative deconfinement phase with fractional-statistics excitations.     

Density functional theory analysis of reactivity of PtxPdy alloy clusters

We investigate the reactivity of various Pt_xPd_y combinations (with x + y = 10 and various x:y ratios) towards the adsorption of specific intermediates of the oxygen reduction, using the B3PW91 hybrid density functional theory. The reactivity is shown to be not only sensitive to the composition of the cluster, but also to the atomic distribution. The calculations indicate that two different ensembles: one ordered and one randomly mixed, with overall composition Pt₃Pd₇ are thermodynamically more favorable than pure Pt₁₀ for the oxygen reduction reaction. The reasons for this behavior are clearly explained in terms of the atomic and electronic distribution, which makes the Pd atoms to act as electron donors both to Pt atoms and to the adsorbates, thus the reactivity of the Pd atoms in such environment becomes intermediate between Pt and Pd. Moreover, it is found that in a mixed Pt₃Pd₇ state the electronic distribution makes the average atom more similar to Pt than to Pd, whereas in an ordered Pt₃Pd₇ cluster, the average atom is more similar to Pd than to Pt.     

A comprehensive model to predict the microwave spectrum of propyne in the region 17–70 GHz for the ground and v10 = 1, 2, 3, 4, 5 vibrational states

A comprehensive model for predicting rotational frequency components in various v₁₀ vibrational levels of propyne was developed. A number of components of the rotational spectra in the ground and v₁₀ = 1, 2, 3, 4 excited vibrational states of propyne in the frequency range 17–70 GHz have been obtained. Molecular constants for these vibrationally excited states have been determined from more than 100 observed rotational transitions. From these experimentally observed components and a model based upon first principals for C_3v molecules, rotational constants have been expressed in a form which enables one to predict rotational components for vibrational levels for propyne up to v₁₀ = 5. The model also appears to be useful in predicting rotational components in more highly excited vibrational levels but data were not available for comparison with the theory. Experimentally measured frequencies are presented and compared with those calculated using the results of basic perturbation theory.     

Elastic stress fields caused by a dislocation in Ge x Si1−x /Si film-substrate system

The elastic stress fields caused by a dislocation in Ge_xSi_(1-x) epitaxial layer on Si substrate are investigated in this work. Based on the previous results in an anisotropic bimaterial system,the image method is further developed to determine the stress field of a dislocation in the film-substrate system under coupled condition. The film-substrate system is firstly transformed into a bimaterial system by distributing image dislocation densities on the position of the free surface. Then,the unknown image dislocation densities are solved by using boundary conditions,i.e.,traction free conditions on the free surface. Numerical simulation focuses on the Ge0.1Si0.9/Si film-substrate system. The effects of layer thickness,position of the dislocation and crystallographic orientation on the stress fields are discussed. Results reveal that both the stresses σxx,σxz at the free surface and the stress σxy,σyy,σyz on the interface are influenced by the layer thickness,but the former is stronger. In contrast to the weak dependence of stress field on the crystallographic orientation the stress field was strongly affected by dislocation position. The stress fields both in the film-substrate system and bimaterial system are plotted.     

Effect of Three Nucleon Forces in p − 3He Scattering

The effect of the inclusion of different models of three nucleon (3N) forces in p ? ³He elastic scattering at low energies is studied. Two models have been considered: one derived from effective field theory at next-to-next-to-leading order and one derived from a more phenomenological point of view—the so-called Illinois model. The four nucleon scattering observables are calculated using the Kohn variational principle and the hyperspherical harmonic technique and the results are compared with available experimental data. We have found that with the inclusion of both 3N force models the agreement with the experimental data is improved, in particular for the proton vector analyzing power A _y .     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory

The nonsymmetric Kaluza-Klein theory unifying Moffat's theory of gravitation, the Yang-Mills' field and the Higgs' fields are constructed in a geometric manner. Spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory are discussed. The connection between R₊ invariance (dilatation on the space-time) from Moffat's theory of gravitation and U(1)_F from GUTs, is proposed within the framework of fermion number conservation.     

Theoretical calculations of H2O linewidths and pressure shifts: Comparison of the Anderson theory with quantum many-body theory for N2 and air-broadened lines

Comparisons of theoretical predictions for line-widths and pressure shifts of water vapor transitions broadened by N₂ or air are presented using the Anderson-Tsao-Curnutte (ATC) theory of pressure broadening and a more recent formalism derived by using quantum many-body techniques. The theoretical predictions are also compared to available experimental results, including 110 measurements of half widths, and eight measured ν₂-band line shifts. The standard ATC theory for multipole interactions is generalized to yield second-order pressure shifts. It is also shown that a scaling transformation from the momentum transfer variable to the impact parameter variable converts the quantum theory to a form very similar to the ATC equations. The essential modification is to replace the ATC resonance functions ?(k), F(k) by new functions g(k), G(k), which, however, have a very different shape. In particular, g(k) is a Gaussian, which results from the simultaneous constraints of a Boltzmann distribution of velocities, coupled with strict momentum and energy conservation in the collision processes. The implication is that highly non-resonant collisions, i.e. collisions involving large inelasticities, are given much less weight in the quantum-derived formalism. The results are analyzed for both high and low J transitions, including the behavior of the anomalously narrow lines measured by Eng and others at high J, and the theoretical dependence of such transitions on the parameter b_min used in the earlier calculations of Benedict and Kaplan. Limited comparisons are made for individual level shifts, and for the temperature dependence of the half width Some specific suggestions for additional experimental studies are also offered.     

Structure of higher order corrections to the Lipatov asymptotic form

High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations, or instantons, of the corresponding functional integrals. For most field theories, the Lipatov asymptotic form has the functional form ca ^NΓ(N+b) (N is the order of perturbation theory) and the relative corrections to it are series in powers of 1/N. It is shown that this series diverges factorially and its high-order coefficients can be calculated using a procedure similar to the Lipatov one: the Kth expansion coefficient has the form const[ln(S ₁/S ₀)]^?K Γ(K+(r ₁? r ₀)/2), where S ₀ and S ₁ are the values of the action for the first and second instantons of this particular field theory, and r ₀ and r ₁ are the corresponding number of zeroth-order modes; the instantons satisfy the same equation as in the Lipatov method and are assumed to be renumbered in order of their increasing action. This result is universal and is valid in any field theory for which the Lipatov asymptotic form is as specified above.     

Geometry of Higgs and Toda fields on Riemann surfaces

We discuss geometrical aspects of Higgs systems and Toda field theory in the framework of the theory of vector bundles on Riemann surfaces of genus greater than one. We point out how Toda fields can be considered as equivalent to Higgs systems — a connection on a vector bundle E together with an End(E)-valued one form both in the standard and in the Conformal Affine case. We discuss how variations of Hodge structures can arise in such a framework and determine holomorphic embeddings of Riemann surfaces into locally homogeneous spaces, thus giving hints to possible realizations of W_n-geometries.     

The renormalized variational theory: Its structure,interpretation, and relation to other methods

We apply the Ritz variational principle to a renormalized form of the Iwamoto-Yamada cluster expansion, restricting our discussion to infinite systems. The structure of the resulting theory is governed by the renormalization which keeps track of the normalization denominator in the expectation value. The single-particle potential for hole states (u_i) is introduced as a Lagrange multiplier in the variational principle, and the self-consistent choice of u_i guarantees that the renormalization factors are determined correctly. The importance of the renormalization is illustrated by a discussion of the two-body approximation to our theory. The general formalism is evaluated in more detail for the representation Ψ_T = exp(S)Φ of the trial wave function. Very fundamental considerations show that the theory is especially adapted to that choice of Ψ_T. In addition, if we use that choice of Ψ_T the self-consistent single-particle energies are directly related to experiment, and the theory is almost identical to renormalized Brueckner theory. Thus we are able to clarify many aspects of the latter. We also discuss the relation to the theory of Coester and Kümmel.     

Some aspects of a unified approach to gauge,dual and Gribov theories

We consider quantum chromodynamics (QCD) with N_c colours and N_f flavours. Large N expansions for this theory are discussed and their advantages are pointed out, especially in relation to the possibility of unifying gauge, dual and Gribov theories of strong interactions. We first recall how the 1/N_c expansion of 't Hooft can be related to a dual loop expansion with a fixed coupling constant. We point out the necessity for quarkless (purely gluonic) bound states to appear and their importance in maintaining confinement at higher orders in 1/N_c. We show how non-orientable dual loops are reinterpreted in QCD and how a paradox appears when N_f is such that asymptotic freedom is lost. Some recent results of Cornwall and Tiktopoulos are analyzed in leading order in 1/N_c. We then introduce a 1/N expansion at ? ≡ N_f/N_c fixed and show how it is related to the hadronic topological expansion (TE). This allows an unambiguous definition of reggeon field theory concepts such as the bare pomeron and diffractive dissociation in QDC. We are able to relate the parameter ? to the clustering of hadronic final states into resonances. Decreasing ? corresponds to increasing cluster over gap size. Renormalization of the dual coupling constant as a function of ? is discussed and an apparent paradox is resolved. We are also able to shed some new light on the problem of f extinction in the TE.Finally, we compare our approach to other schemes trying to relate different aspects of hadron physics.