Color dielectric model with two scalar fields

SU(2) Yang-Mills theory coupled in a non-minimal way to two scalar fields is discussed. For the massless scalar fields a family of finite energy solutions generated by an external, static electric charge is found. Additionally, there is a single solution which can be interpreted as a confining one. Similar solutions have been obtained in the magnetic sector. In the case of massive scalar fields the Coulomb problem is investigated. We find that asymptotic behavior of the fields can also, for some values of the parameters of the model, give confinement of the electric charge. Quite interestingly one glueball-meson coupling gives the linear confining potential. Finally, it is shown how, for one non-dynamical scalar field, we can derive the color dielectric generalization of the Pagels-Tomboulis model.Received: 22 April 2003, Published online: 12 September 2003     

How to determine an effective potential for a variable cosmological term

It is shown that if a variable cosmological term in the present Universe is described by a scalar field with minimal coupling to gravity and with some phenomenological self-interaction potential V(ϕ), then this potential can be unambiguously determined from the following observational data: either from the behavior of density perturbations in dustlike matter component as a function of redshift (given the Hubble constant additionally), or from the luminosity distance as a function of redshift (given the present density of dustlike matter in terms of the critical value). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 721–726 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

An Exact Inflationary Solution to Non-Minimally Coupling

We find a new exact inflationary solution to non-minimally coupled scalar field from a specific H(φ). The inflation is driven by the evolution of the scalar field with a new inflation potential. The spectral index of the scalar density fluctuations n _s is consistent with the result of WMAP3 for the power-law flat ΛCDM model. Our solution relaxes the constraint to the quartic coupling constant, e.g. when ξ=10³, λ≤8.9×10⁻¹¹.     

Self Duality Equations for Ginzburg–Landau¶and Seiberg–Witten Type Functionals¶with 6th Order Potentials

The abelian Chern–Simons–Higgs model of Hong-Kim-Pac and Jackiw–Weinberg leads to a Ginzburg–Landau type functional with a 6^th order potential on a compact Riemann surface. We derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0, for any number of prescribed vortices. We also introduce a Seiberg–Witten type functional with a 6^th order potential and again show the existence of two asymptotically different solutions on a compact K?hler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations. Received: 13 October 1998 / Accepted: 21 October 2000     

Exploring effects of strong interactions in enhancing masses of dynamical origin

A previous study of the dynamical generation of masses in massless QCD is considered from another viewpoint. The quark mass is assumed to have a dynamical origin and is substituted for by a scalar field without self-interaction. The potential for the new field background is evaluated up to two loops. Expressing the running coupling in terms of the scale parameter μ, the potential minimum is chosen to fix m _top=175 GeV when μ ₀=498 MeV. The second derivative of the potential predicts a scalar field mass of 126.76 GeV. This number is close to the value 114 GeV, which preliminary data taken at CERN suggested to be associated with the Higgs particle. However, the simplifying assumptions limit the validity of the calculations done, as indicated by the large value of a = \frac g²4p=1.077 \alpha=\frac {g^{2}}{4\pi}=1.077 obtained. However, supporting statements about the possibility of improving the scheme come from the necessary inclusion of weak and scalar field couplings and mass counterterms in the renormalization procedure, in common with the seemingly needed consideration of the massive W and Z fields, if the real conditions of the SM model are intended to be approached.     

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.     

Bound-State Solutions of the Klein-Gordon Equation for the Generalized <Emphasis Type="Italic">PT</Emphasis>-Symmetric Hulthén Potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. PACS numbers: 03.65.Fd, 03.65.Ge     

Trapping the Kaluza-Klein scalar

The Kaluza-Klein unified theory predicts the existence of a Brans-Dicke type scalar field with = 0. Solar system experiments do, however, imply that gravitational scalar fields must be suppressed either by a very weak coupling to matter ( > 500) or a self-interaction. Here the consequences of a self-interaction potential of the Kaluza-Klein scalar are investigated. By suppressing the scalar field in this way, the one-body metric reduces to the Schwarzschild solution. The cosmologies of the scalar-tensor model are, however, very different from cosmologies of Einstein's theory, since here the time evolution of the cosmic scale-factor is determined only by the initial conditions. These may be chosen so that the theory is compatible with the hypothesis of primordial nucleosynthesis.     

Pseudospin symmetry for modified Rosen-Morse potential including a Pekeris-type approximation to the pseudo-centrifugal term

By a novel algebraic method we study the approximate solution to the Dirac equation with scalar and vector second P?schl-Teller potential carrying spin symmetry. The transcendental energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. It is found that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter a \alpha goes to zero. The equally scalar and vector case is studied briefly.     

General models of Einstein gravity with a non-Newtonian weak-field limit

We investigate Einstein theories of gravity, coupled to a scalar field j{\varphi} and point-like matter, which are characterized by a scalar field-dependent matter coupling function e^H(j){e^{H(\varphi)}} . We show that under mild constraints on the form of the potential for the scalar field, there are a broad class of Einstein-like gravity models—characterized by the asymptotic behavior of H—which allow for a non-Newtonian weak-field limit with the gravitational potential behaving for large distances as ln r. The Newtonian term GM/r appears only as sub-leading. We point out that this behavior is also shared by gravity models described by f (R) Lagrangians. The relevance of our results for the building of infrared modified theories of gravity and for modified Newtonian dynamics is also discussed.     

Scalar mesons and multichannel amplitudes

Properties of scalar–isoscalar mesons are analyzed in a unitary model using separable interactions in three decay channels: $\pi\pi, and an effective . We obtain different solutions by fitting various data on the and phase shifts and inelasticities including the CERN–Cracow–Munich measurements of the reaction on a polarized target. The analytical structure of the meson–meson multichannel amplitudes is studied with special emphasis on the role played by the S-matrix zeroes. S-matrix poles, located in the complex energy plane not too far from the physical region, are interpreted as scalar resonances. We see a wide , a narrow and a relatively narrow . In one of our solutions a resonance at about 1700 MeV is also found. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with available data. We construct an approximation to our model and show that the Breit–Wigner approach has a limited phenomenological applicability. Received: 19 October 1998 / Revised version: 25 January 1999 / Published online: 15 April 1999     

A coupled theory of electromagnetism and gravitation

A coupling electromagnetism with a previously developed scalar theory of gravitation is presented. The principle features of this coupling are: (1) a slight alteration to the Maxwell equations, (2) the motion of a charged particle satisfies an equation with the Lorentz force-appearing on the right side in place of zero, and (3) the energy density of the electromagnetic field appears in the gravitational field equation in a manner similar to the mass term in the Klein-Gordonequation. The field of a static, spherically symmetric charged particle is computed. The electromagnetic field gives rise to l/r ² terms in the gravitational potential.     

Two-pion production processes, chiral symmetry and NN interaction in the medium

We study the two-pion propagator in the nuclear medium. This quantity appears in the ππ T-matrix and we show that it also enters the QCD scalar susceptibility. The medium effects on this propagator are due to the influence of the individual nucleon response to a scalar field through their pion clouds. This response is appreciably increased by the nuclear environment. It produces an important convergence effect between the scalar and pseudoscalar susceptibilities, reflecting the reshaping of the scalar strength observed in 2π production experiments. While a large modifications of the σ propagator follows, due to its coupling to two pion states, we show that the NN potential remains instead unaffected.     

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans–Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power–law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant, [(w)\tilde]{\tilde{\omega}} . We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For non-constant scalar fields and spatially flat geometries, solutions are found to be in the form of power–law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The power–law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power–law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the condition ${\tilde{\omega} > -3/2}${\tilde{\omega} > -3/2} which prevents ghost scalar fields in the equivalent 4D vacuum Brans–Dicke equations. The results are presented in a few tables and figures.     

Periodic Distribution of Galaxies in Generalized Scalar Tensor Theory

With the help of Nordtvedt's scalar tensor theory an exact analytic model of a non–minimally coupled scalar field cosmology in which the gravitational coupling G and the Hubble factor H oscillate during the radiation era is presented. A key feature is that the oscillations are confined to the early stages of the radiation dominated era with G approaching its present constant value while H becoming a monotonically decreasing function of time. The Brans Dicke parameter is chosen to be a function of Brans Dicke scalar field so that no conflict with observational constraints regarding its present value arises.     

Generalized spin and pseudo-spin symmetry: Relativistic extension of supersymmetric quantum mechanics

We consider the Dirac equation in 1+1$1+1$ space–time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples.     

Flavour dynamics with general scalar fields

We consider a spontaneously broken gauge theory based on the standard model (SM) group with scalar fields that carry arbitrary representations of G, and we investigate some general properties of the charged and neutral current involving these fields. In particular we derive the conditions for having real or complex couplings of the Z boson to two different neutral or charged scalar fields, and for the existence of CP-violating Z-scalar-scalar couplings. Moreover, we study models with the same fermion content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of Higgs doublets. We show that the structure of the Z-Higgs boson and of the Yukawa couplings in these models can be such that CP-violating form factors which conserve chirality are induced at the one-loop level. Received: 18 December 1998 / Published online: 22 March 1999     

Dynamical Evolution of a Scalar Field Coupling to Einstein’s Tensor in Charged Braneworld Black Holes

In this work, we study the quasinormal modes (QNMs) of scalar field coupling to Einstein’s tensor in charged braneworld black hole. The shape of the potential function is illustrated and we find that lower coupling constant leads to more stable field. We then apply six-order WKB approximation to calculate the quasinormal frequencies (QNF) in weaker coupling field, and depict the dependence of the oscillation frequency on the coupling constant. Furthermore, we use finite difference method to shape the evolution of the coupling field and find that coupling field with lower multipole numbers l corresponds to stable field, while higher l tends to lead to instability when the coupling constant is larger than a threshold value. Finally the fitting curve of such threshold value is given numerically.     

Asymptotic Interactions of Critically Coupled Vortices

 At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. Here, a formula for the asymptotic metric for two well separated vortices is obtained, which depends on a modified Bessel function. A straightforward extension gives the metric for N vortices. The asymptotic metric is also shown to follow from a physical model, where each vortex is treated as a point-like particle carrying a scalar charge and a magnetic dipole moment of the same magnitude. The geodesic motion of two well separated vortices is investigated, and the asymptotic dependence of the scattering angle on the impact parameter is determined. Formulae for the asymptotic Ricci and scalar curvatures of the N-vortex moduli space are also obtained. Received: 25 June 2002 / Accepted: 7 February 2003 Published online: 17 April 2003 Communicated by A. Kupiainen     

Generalized heavy baryon chiral perturbation theory

Standard SU(2) Heavy Baryon Chiral Perturbation Theory is extended in order to include the case of small or even vanishing quark condensate. The effective lagrangian is given to in its most general form and to in the scalar sector. A method is developed to efficiently construct the relativistic baryonic effective lagrangian for chiral SU(2) to all orders in the chiral expansion. As a first application, mass- and wave-function renormalization as well as the scalar form factor of the nucleon is calculated to . The result is compared to a dispersive analysis of the nucleon scalar form factor adopted to the case of a small quark condensate. In this latter analysis, the shift of the scalar form factor between the Cheng-Dashen point and zero momentum transfer is found to be enhanced over the result assuming strong quark condensation by up to a factor of two, with substantial deviations starting to be visible for . Received: 22 July 1998 / Revised version: 2 September 1998 / Published online: 2 November 1998