On the Rainich geometrization of a vector meson field in the Kibble theory

The variables of a vector meson field are determined within the framework of the Kibble theory as the functions of the metric tensor, affine connection and their derivatives and a system of differential equations is found for the metric tensor and affine connection which is equivalent to the equations of motion of gravitational and vector meson fields.     

The Rainich conditions for neutrino fields

The algebraic Rainich conditions for neutrino fields are obtained in terms of an algebraic classification of symmetric second-rank tensors. The differential Rainich conditions are also obtained for ail but one class of neutrino fields. The algebraic classification of symmetric second-rank tensors used here is compared to two previously published classifications. The Weyl square of a symmetric second-rank tensor is introduced and the Petrov type of the Weyl square is used to give a method for determining the class of the symmetric tensor.     

On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.     

Towards light scalar meson structure

The origin of the lightest scalar mesons is studied in the framework of the instanton liquid model of the QCD vacuum. The impact of phonon-like vacuum excitations on the σ-meson features is qualitatively analyzed. In particular, it is noticed that the changes produced in the scalar sector may unexpectedly become quite considerable in spite of insignificant values of corrections to the dynamical quark masses and then the medley of σ-meson and those excitations may reveal itself as broad resonance states of different masses.     

Multiquark states and the mixing of scalar meson

In order to describe Kaon-Nucleon scattering data, the mixing of scalar meson σ_0 and σ_8 must be introduced in the chiral SU(3) quark model. Inspired by this, now the mixing of scalar meson is further considered to study some interesting dibaryons in the chiral SU(3) quark model. The results show that the mixing of scalar meson has different effects on these dibaryons.     

On the geometrization of quantum mechanics

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.     

Towards resolution of the scalar meson nonet enigma

By the application of a linear mass spectrum to a composite system of both the pseudoscalar and scalar meson nonets, we find three relations for the masses of the scalar states which suggest the assignment for the scalar meson nonet a₀(1320), K ₀ ^* (1430), f₀(1500), and f₀ ^′(980).     

Mixing of scalar meson and baryon-baryon interaction

At quark level,we study the effect of ideal mixing of singlet σ 0 and octet σ 8 scalar mesons on baryon-baryon interaction in the chiral SU(3) quark model.We solve the resonating group method equation for scattering process and bound state.The results show that the binding energy of deuteron and nucleonnucleon and hyperon-nucleon scattering data can be reasonably described for ideal mixing.Taking the same parameters we used in the scattering calculation,we further investigate the possible dibaryons and find the binding energy of (ΩΩ) ST =00 and (Ξ *Ω) ST =0 1 2 can be reduced a lot for ideal mixing.     

Secondary vacuum trajectories and scalar meson exchange

A new second vacuum trajectory passing throughf*(1515) and σ(548), α(t)=? 0.3+t, is proposed, which, together with α_p″(t=0)=? 0.5, overcomes the failure of Igi's original superconvergent πN sum rule and avoids the ghost-state of the conventionalP′-trajectory. The negative residue att=0 confirms the repulsive contribution of a vacuum pole component withJ=0 to the generalizeds-reaction potential, as postulated by Chew (1965). TheP- andP′-poles can build the non resonating background. The Gell-Mann nonsense mechanism at the negative integers with wrong signature explains the dips in the elastic π^± p-scattering att=?0.7, ?2.7 and ?4.5 (GeV/c)². σ(∞) for πN reactions turns out to be 24.3 mb, if α _p (t=0)=1, but the best fits to the total πN cross sections for pion momenta between 2 and 29 GeV/c yield α _p (t=0)=0.93.     

A possible assignment for the ground scalar meson nonet

Based on the main assumption that a₀(980) and D ^* _sJ(2317) belong to the 1³P₀ q¯ multiplet, in the framework of Regge phenomenology and meson-meson mixing, it is suggested that a₀(980), K ^* ₀(1052), f₀(1099) and f₀(530) constitute the ground scalar meson nonet, and that the f₀(1099) is composed mostly of s¯, while the f₀(530) is mainly a u¯ + d¯ system. It is supposed that these states would likely correspond to the observed scalar states a₀(980), κ(900), f₀(980) and f₀(600)/σ, respectively. The agreement between the present findings and those given by other different approaches is satisfactory.     

Two-photon mechanism of scalar meson production by colliding beams

Cross sections of scalar mesons f ₀(980), a ₀(980), and σ(600) production by colliding electron-positron beams are calculated. Two-photon decay widths of scalar mesons obtained in the Nambu-Jona-Lasinio model are used with quark and meson loops taken into account.     

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein–Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a Dirac term in the Einstein–Hilbert action. For sufficient complicated links and knots, there are “connecting tubes” (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1) × SU(2) ×?SU(3).     

Identification of the glueballs and the scalar meson nonet of lowest mass

We discuss the theoretical expectations and phenomenological evidence for the lightest glueballs and the members of the meson nonet with quantum numbers . We reconsider the recent evidence for candidate states with masses below 1700 MeV, but include also the results from earlier phase-shift analyses. Arguments are presented to classify the scalars and as members of the nonet, with a mixing rather similar to that of the pseudoscalars and . The S-wave states called and are considered as different signals from a single broad resonance, which we take to be the lowest-lying glueball. This state together with and with spin form the basic triplet of binary gluonic bound states. We argue that these hypotheses are consistent with what can be expected theoretically. Received: 30 November 1998 / Revised version: 17 February 1999 / Published online: 27 April 1999     

Vector and scalar meson resonances inK→πππ decays

Corrections toK→πππ decays induced by vector and scalar meson exchange are investigated within chiral perturbation theory. The widths of scalar mesons are analyzed and their influence onK→πππ parameters were examined. The overall corrections were found to be parameter dependent, but contributing in some cases as much as 10%.