Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff

In this paper we discuss the Eliashberg equations for the case of an electron-phonon coupling with an energy cutoff. This cutoff is imposed either for the energy difference by means of a strip function, or for both energies, with a Cooper-like expression. The strip function cutoff requires explicit calculation of not only the frequency renormalization functionZ but also the energy renormalizationX. The physical origin of such cutoffs might lie in the very strong electron-electron interaction which seems typical for highT _c superconductivity. If such cutoffs are admitted, the hypothesis thatT _c is caused at least in part by a strong electron-phonon interaction can be reconsidered. We find that the combination of strong coupling and low-energy cutoff could produce highT _c with only small isotope effect and with little damping or pulling of the phonon modes. Correlation with other physical properties, such as specific heat, is reexamined in view to estimate the coupling constant . Some objections to the model using strong electron phonon interaction are removed and better agreement with observed properties is obtained     

Numerical Method for Solving Two-Body Bound-State Bethe-Salpeter Equations for Unequal Constituent Masses

 A theoretical technique is developed for obtaining finite-energy numerical solutions to a class of two-body, bound-state Bethe-Salpeter equations in the ladder approximation when the constituent masses are unequal. The class of equations is restricted to those for which the Bethe-Salpeter equation can be written as a differential equation and to situations where the coupling constant is real. Such equations can result when the binding force is created by the exchange of a massless quanta. The theoretical technique is tested numerically by obtaining finite-energy solutions of the partially-separated Bethe-Salpeter equation describing the unequal-mass Wick-Cutkosky model in the ladder approximation. Received February 19, 1997; Revised April 2, 1998; accepted for publication October 30, 1998     

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin–Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number. Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001     

Localization of matters on the bent brane in bulk

We investigate the possibility of localizing various matter fields on a bent AdS₄ (dS₄) thick brane in AdS₅. For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.     

Flow characteristics around a square cylinder with changing chamfer dimensions

Abstract  

It is known that for a square cylinder subjected to uniform flow, the drag force changes with the angle of attack. To clarify the flow characteristics around a square cylinder with corner cutoffs, we measured the drag coefficient and the Strouhal number for changing chamfer dimensions. We analyzed the flow around a square cylinder with corner cutoffs by applying the RNG k–ε turbulent model, and investigated the surface flow pattern using visualization by means of the oil film and mist flow method. From these results, we obtained the surface flow patterns by the oil film method and numerical analysis. The numerical results agreed well with the experimental values. The drag coefficient of the square cylinder with corner cutoffs decreased suddenly at an angle of attack of about α = 0°– 10° when compared with the drag coefficient for a square cylinder. The minimum value of the drag coefficient for the square cylinder with corner cutoffs decreased by about 30% compared with that for the square cylinder. The drag coefficient of the square cylinder with 10% corner cutoffs was found to be smallest, since the wake area of this square cylinder was smaller compared with that of the other square cylinder.     

Expanding and collapsing scalar field thin shell

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr?m geometry. The Israel junction conditions between Reissner-Nordstr?m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien–Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when p is an explicit function of R. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.     

The perturbative proton form factor reexamined

We recalculate the proton Dirac form factor based on the perturbative QCD factorization theorem, which includes Sudakov suppression. The evolution scale of the proton wave functions and the infrared cutoffs for the Sudakov re-summation are carefully chosen such that the soft divergences from large coupling constants are diminished and perturbative QCD predictions are stabilized. We find that the King–Sachrajda model for the proton wave function leads to results which are in better agreement with experimental data than those from the Chernyak–Zhitnitsky wave function. Received: 27 November 1998 / Published online: 7 April 1999     

Dynamo Effect in the Kraichnan Magnetohydrodynamic Turbulence

The existence of a dynamo effect in a simplified magnetohydrodynamic model of turbulence is considered when the magnetic Prandtl number approaches zero or infinity. The magnetic field is interacting with an incompressible Kraichnan-Kazantsev model velocity field which incorporates also a viscous cutoff scale. An approximate system of equations in the different scaling ranges can be formulated and solved, so that the solution tends to the exact one when the viscous and magnetic-diffusive cutoffs approach zero. In this approximation we are able to determine analytically the conditions for the existence of a dynamo effect and give an estimate of the dynamo growth rate. Among other things we show that in the large magnetic Prandtl number case the dynamo effect is always present. Our analytical estimates are in good agreement with previous numerical studies of the Kraichnan-Kazantsev dynamo by Vincenzi (J. Stat. Phys. 106:1073–1091, 2002).     

Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime

We demonstrate the possibility of removing the divergences in the energy-momentum tensor by identifying divergent terms with renormalizations of the coupling constants in the gravitational field equation, modified to include a cosmological term and terms quadratic in the curvature. The model studied is that of a classical Robertson-Walker metric and a quantized minimally coupled neutral scalar field. The theory is constructed first with an ultraviolet cutoff as a phenomenological ansatz. The cutoff is then removed in an attempt to obtain a more fundamental theory, whereupon the question arises of the covariance and uniqueness of the resulting renormalized energy-momentum tensor. In the case of a massless field in a spatially flat universe, an apparent infrared divergence is discussed from the point of view of operational determination of the renormalized coupling constants. In the other cases, although the divergences are successfully accounted for by renormalization, we are left with finite leading terms which do not appear to be identifiable with geometrical tensors; the significance of this result is under investigation. If these anomalous terms are dropped, the renormalized energy-momentum tensor agrees with that defined by adiabatic regularization, provided that the limit of slow time variation taken in that method is generalized to a limit of “spacetime flatness.”     

Dual models for non-hadrons

The possibility of describing particles other than hadrons (leptons, photons, gauge bosons, gravitons, etc.) by a dual model is explored. The Virasoro-Shapiro model is studied first, interpreting the massless spin-two state of the model as a graviton. We prove that in the limit of zero slope (with g_vs²α′ held fixed) one obtains the Einstein theory of gravitation accompanied by a massless scalar field. Next, the Veneziano model is studied for small slope as an expansion in powers of α′. It is known from previous work that the zeroth order term is precisely the Yang-Mills theory of a multiplet of massless vector bosons. We show that there are order α′ terms arising both from the dual tree and loop graphs. The former constitutes a relatively unimportant modification of the Yang-Mills theory, whereas the latter involves the coupling of the massless scalar and graviton states of the Virasoro-Shapiro model. Thus one may take the point of view that gravity arises as a unitarization effect in a dual unified theory of electromagnetism and weak interactions. In order to obtain the correct values for the electric charge and Newton's constant it is necessary that α′ ? 10^?34 GeV^?2 The coupling of massless scalar states is also studied.     

Two-dimensional quantum ring in a graphene layer in the presence of a Aharonov–Bohm flux

In this paper we study the relativistic quantum dynamics of a massless fermion confined in a quantum ring. We use a model of confining potential and introduce the interaction via Dirac oscillator coupling, which provides ring confinement for massless Dirac fermions. The energy levels and corresponding eigenfunctions for this model in graphene layer in the presence of Aharonov–Bohm flux in the centre of the ring and the expression for persistent current in this model are derived. We also investigate the model for quantum ring in graphene layer in the presence of a disclination and a magnetic flux. The energy spectrum and wave function are obtained exactly for this case. We see that the persistent current depends on parameters characterizing the topological defect.     

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams for the massless ϕ ³ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of the Lipatov integrable chain model. The text was submitted by the authors in English.     

Critical Behavior of Massless Free Field at Depinning Transition

We consider the d-dimensional massless free field localized by a δ-pinning of strength ɛ. We study the asymptotics of the variance of the field (when d= 2), and of the decay-rate of its 2-point function (when d≥ 2), as ɛ goes to zero, for general Gaussian interactions. Physically speaking, we thus rigorously obtain the critical behavior of the transverse and longitudinal correlation lengths of the corresponding d+ 1-dimensional effective interface model in a non-mean-field regime. We also describe the set of pinned sites at small ɛ, for a broad class of d-dimensional massless models. Received: 1 November 2000 / Accepted: 15 June 2001     

Cosmological aspects of the gravitational interaction of a scalar field in the affine-metric theory of gravitation

The gravitational interaction of a scalar field, with allowance for the possible influence of the torsional and nonmetric nature of space-time, is investigated within the framework of the affine-metric theory of gravitation. The equations of the theory are derived from the variational principle. It is shown that in an affine-metric space, the combined Lagrangian of the gravitational and scalar fields with conformal coupling is reduced to the Lagrangian of the system of gravitational and axion fields in the general theory of relativity. All of the exact general solutions of the consistent system of equations of gravitational and scalar (massless) fields in the affine-metric space under consideration are obtained for all types of homogeneous Friedmann cosmological models, with the initial singularity being removed from some of them. Homogeneous, anisotropic cosmological models, for which all of the exact general solutions are also obtained, are investigated. Some of these models are nonsingular, and the effect of isotropization due to the torsional and nonmetric nature of space-time occurs for many of them. K. D. Ushinskii State Pedagogical University, Yaroslavl’. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–50, May, 1998.     

The fifth interaction: universal long range force between spins

In this paper we present a review of our investigations on universal long range force between spins mediated by a massless axial vector gauge field which we name as “axial photon”. The invariance of the Lagrangian field theory of particles, possessing spin degrees of freedom, under local Lorentz transformations, necessitates the introduction of such an axial vector gauge field which interacts with spin current of the particles. Classical as well as quantum dynamics of electrons interacting with photon and axial photon are worked out. The new interaction is found to be asymptotically free. It is shown thatqed can be made finite if the coupling strengths of electron to photon and axial photon can be made equal. Experimental consequences of the existence of axial photon are discussed and the strength of the interaction is estimated by comparing predictions of the theory with experiments.     

Electronic states on the surface of graphite

Graphite consists of graphene layers in an AB (Bernal) stacking arrangement. The introduction of defects can reduce the coupling between the top graphene layers and the bulk crystal producing new electronic states that reflect the degree of coupling. We employ low temperature high magnetic field scanning tunneling microscopy (STM) and spectroscopy (STS) to access these states and study their evolution with the degree of coupling. STS in magnetic field directly probes the dimensionality of electronic states. Thus two-dimensional states produce a discrete series of Landau levels while three-dimensional states form Landau bands providing a clear distinction between completely decoupled top layers and ones that are coupled to the substrate. We show that the completely decoupled layers are characterized by a single sequence of Landau levels with square-root dependence on field and level index indicative of massless Dirac fermions. In contrast weakly coupled bilayers produce special sequences reflecting the degree of coupling, and multilayers produce sequences reflecting the coexistence of massless and massive Dirac fermions. In addition we show that the graphite surface is soft and that an STM tip can be quite invasive when brought too close to the surface and that there is a characteristic tip-sample distance beyond which the effect of sample-tip interaction is negligible.     

No‐go result for supersymmetric gauge theories in the causal approach

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non‐Abelian gauge theory (SUSY‐QCD) is uniquely determined by some natural assumptions, as in the case of Yang‐Mills models. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.     

Existence and Uniqueness Theorems for Massless Fields on a Class of Spacetimes with Closed Timelike Curves

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC’s), in which all future-directed CTC’s traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in L ₂ on ℐ ⁻ , we prove existence of smooth solutions which are regular at null and spatial infinity (have finite energy and finite L ₂ -norm) and have the given initial data on ℐ ⁻ . A restricted uniqueness theorem is obtained, applying to solutions that fall off in time at any fixed spatial position. For a complementary class of spacetimes in which CTC’s are confined to a compact region, we show that when solutions exist they are unique in regions exterior to the CTC’s. (We believe that more stringent uniqueness theorems hold, and that the present limitations are our own.) An extension of these results to Maxwell fields and massless spinor fields is sketched. Finally, we discuss a conjecture whose meaning is essentially that the Cauchy problem for free fields is well defined in the presence of CTC’s whenever the problem is well-posed in a geometric-optics limit. We provide some evidence in support of this conjecture, and we present counterexamples that show that neither existence nor uniqueness is guaranteed under weaker conditions. In particular, both existence and uniqueness can fail in smooth, asymptotically flat spacetimes with a compact nonchronal region. Received: 28 November 1994/Accepted: 20 May 1996     

A path integral formula for quark condensate states in?a?modified?PQCD

A modified version of PQCD considered in previous works is investigated here in the case of retaining only the quark condensate. The Green function generating functional is expressed in a form in which Dirac’s delta functions are now absent from the free propagators. The new expansion implements the dimensional transmutation effect through a single interaction vertex in addition to the standard ones in massless QCD. The new vertex suggest a way for constructing an alternative to the SM, in which the mass and CKM matrices could be generated by the instability of massless QCD under the production of the top quark and other fermions condensates, in a kind of generalized Nambu–Jona-Lasinio mechanism. The results of a two loop evaluation of the vacuum energy indicate that the quark condensate is dynamically generated. However, the energy as a function of the condensate parameter is again unbounded from below in this approximation. Assuming the existence of a minimum of the vacuum energy at the experimental value of the top quark mass m _q =173 GeV, we evaluate the two particle propagator in the quark–anti-quark channel in zero order in the coupling and a ladder approximation in the condensate vertex. Adopting the notion from the former top quark models in which the Higgs field corresponds to the quark condensate, the results suggest that the Higgs particle could be represented by a meson which might appear at energies around twice the top quark mass.     

Entropic Repulsion of the Massless Field with a Class of Self-potentials

We consider the d+1-dimensional effective interface model of gradient type with a quadratic interaction potential and a self-potential. Without the self-potential, the model coincides with the d-dimensional massless Gaussian field. We show that for an arbitrary repulsive self-potential which can be thought as interaction of the interface with a “soft wall”, the field is pushed up at least to the same level when the original Gaussian field is conditioned to be positive everywhere, namely the “hard wall” condition is imposed.