A variant of the Stückelberg formalism for massive gauge fields and applications

A variant of the Stückelberg formalism for massive neutral and non- Abelian gauge fields studied in detail. Applications to hadron electrodynamcs. are discussed. The major new results is that if the isovector, hadronic, electroma magnetic current is proportional to the neutral ? meson field operator, the finite c-number Schwinger term in the current commutators can be eliminated altogether by introducing an unphysical, negative metric, scalar particle without violating unitarity.     

Massive mesons in Weyl–Dirac theory

In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl–Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton–Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.     

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.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

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.     

Current algebra derivation of temperature dependence of hadron couplings with currents

The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature were obtained by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived by applying the method of current algebras and the hypothesis of partial conservation of axial-vector currents. The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the ρωπ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Properties of vector and axial-vector mesons from a generalized Nambu-Jona-Lasinio model

We construct a generalized Nambu-Jona-Lasinio lagrangian including scalar, pseudoscalar, vector and axial-vector mesons. We specialize to the two-flavor case. The properties of the structured vacuum as well as meson masses and coupling constants are calculated giving an overall agreement within 20% of the experimental data. We investigate the meson properties at finite density. In contrast to the mass of the scalar σ-meson, which decreases sharply with increasing density, the vector meson masses are almost independent of density. Furthermore, the vector-meson-quark coupling constants are also stable against density changes. We point out that these results imply a softening of the nuclear equation of state at high densities. Furthermore, we discuss the breakdown of the KFSR relation on the quark level as well as other deviations from phenomenological concepts such as universality and vector meson dominance.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

Construction of local meson operator from the path-ordered operator in QCD2

A local meson operator is constructed from the path-ordered operator on QCD₂. The meson operator satisfies the Klein-Gordon equation with the mass identical to the eigenvalue of the 't Hooft equation. The interaction of the meson is shown to be nonlocal and to have a coupling proportional to 1/N_c.     

Spinor strong interaction model for meson spectra

A model for a bound quark-antiquark system is constructed from quark spinor equations and the associated pseudoscalar massless interaction potential equations in a way departing from conventional relativistic quantum mechanics. From the so-constructed covariant meson equations, linear confinement arises naturally. Nonlinear radial equations for the pseudoscalar and vector mesons in the rest frame are derived without approximation. An internal complex space is introduced for representation of the quark flavors. Quark masses are generalized to operators operating on functions in this space. A simple model is proposed for the meson internal functions and mass operators producing the squares of the average quark masses as eigenvalues. The present space-time model calls for a particle classification scheme different from the usual nonrelativistic one. When combined with the internal model, it may account for the gross structure of the meson spectra together with the form of an empirical relation. Upper limits of bare quark masses are estimated from simplified analytical solutions of the radial equations and agree approximately with the bare quark masses obtained from baryon data in a companion paper. The radial equations are solved numerically yielding estimates of the strong interaction radii of the ground state mesons.     

Soluble model of a single component fermion interacting with a vector meson

A model is formulated in two dimensional spacetime in which a massive vector meson is coupled to only the upper or the lower component of the usual two component fermion field operator. This condition implies a unique (nonconserved) V ± A form for the current, a result which is equivalent to the statement that the current is either self-dual or anti-self-dual. The Green's functions of the model are computed using the device of the external source. A significant result which emerges is the fact that the renormalized meson mass is not a polynomial form in the coupling constant, a situation which has not previously occurred in any of the known soluble field theories. Although there is no limit of this model in which one can obtain the Thirring model, it is shown that a particular solution of the latter can be obtained provided that one considers only configurations in which all fermion excitations are moving to the left or all are moving to the right.     

A relativistic quantum field theoretical model for nuclear slab collision dynamics

We treat the dynamics of colliding nuclear slabs in a relativistic quantum field theory by using the relativistic mean field approximation. Starting from Walecka's lagrangian, the nucleons are represented by single-particle spinors determined by a Dirac equation that contains a repulsive mean vector meson field and an attractive mean scalar meson field. Both fields satisfy Klein-Gordon equations whose source terms are again determined by the nucleon spinors. The two equal nuclear slabs are translationally invariant in two transverse dimensions and consist of spin and isospin symmetric nuclear matter. By specification of appropriate initial conditions for the collision, we numerically solve the system of coupled Dirac and Klein-Gordon equations for lab energies per nucleon up to 420 MeV. For small energies the results are similar to TDHF results. The time dependence of the density distribution, the mean meson fields, and the damping of the collision are studied. At the highest bombarding energy retardation effects are taken into account.     

Nonrelativistic anyons in external electromagnetic field

The first-order, infinite-component field equations we proposed before for nonrelativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

The Bargmann-Wigner method in Galilean relativity

The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling.More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.Research supported in part by the U.S. Atomic Energy Commission.     

Dark energy as a massive vector field

We propose that the Universe is filled with a massive vector field non-minimally coupled to gravitation. The field equations of the model are consistently derived, and their application to cosmology is considered. The Friedmann equations acquire an extra dark-energy component, which is proportional to the mass of the vector particle. This leads to a late-time accelerated de Sitter type expansion. The free parameters of the model (gravitational coupling constants and initial value of the cosmological vector field) can be estimated by using the PPN solar system constraints. The mass of the cosmological massive vector particle, which may represent the main component of the Universe, is of the order of 10^-63 g. PACS 03.70.+k; 11.90.+t; 11.10.Kk     

Inertial Mass and Vacuum Fluctuations in Quantum Field Theory

Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.