Gauge Field Coupling Research Articles

Axion driven baryogenesis

We show that the axion gauge field coupling leads to tachyonic mass generation for the gauge fields when the axion field has a homogeneous and isotropic time dependent (i.e. cosmological) expectation value. In the context of the standard SU (3) × SU (2) × U (1) gauge group, it is possible to eliminate this instability in a thermal equilibrium environment, provided a finite chemical potential is introduced for B+ L. This finite density environment that stabilizes the system, can be generated through B+ L violating processes that take place with a considerable rate in the standard model at TeV temperatures. In this way, through a mechanism where CPT is spontaneously violated, baryogenesis can take place in a thermal equilibrium environment at TeV temperatures.

Diamagnetism in the Gauge theory

A non-perturbative approach to the normal state diamagnetism in the gauge theory is described. A fit the observed normal state diamagnetism is proposed which implies that the dimensionless gauge field coupling constant is in the range 0.02–0.2 for YBaCuO 7.

Inconsistency of spin 4-spin 2 gauge field couplings

The authors invert the usual problem of coupling higher spin gauge fields to gravity by treating (linearised) gravity as the 'matter field' source of spin 4 gauge theory. This is motivated by the existence of the conserved gravitational four-index Bel-Robinson tensor as a possible current for the spin 4 field. They first derive this tensor as a Noether current, thereby linking it to a novel invariance of spin 2. It is then shown that, as usual for higher spins, consistency does not survive beyond lowest-order cubic coupling.

Non-Abelian geometric phase and long-range atomic forces.

Using fully quantal methods, we investigate various manifestations of the geometric phase in bound and free diatom systems. Adiabaticity and degeneracy are not invoked in the discussion.Received 3 May 1989DOI:https://doi.org/10.1103/PhysRevLett.64.256©1990 American Physical Society

Interaction of U(1) cosmic strings: Numerical intercommutation

The putative ability of cosmic strings to act as seeds for galaxies depends on the efficiency of a number of processes that produce an initial network of strings and then allow them to evolve to a population that can act as condensation centers. Here the classical field theory of the interaction of cosmic strings is studied. A limited survey of numerical evolutions has been carried out. Calculations have been carried out showing parallel string–string repulsion; string–antistring (i.e., antiparallel string) annihilation with initial velocity v=0 and v=0.75; string–string collision at right angles with v/c=0.1, 0.5, 0.75, 0.85, 0.9c, with v/c=0.75 at θ=π/4 and at θ=3π/4, and with v/c=0.9 at θ=7π/8; and string–string and string–antistring collisions with v/c=0.9 and v/c=0.95. Intercommutation occurs in all situations so far investigated except that string–antistring collision with v/c≳0.90 apparently leads to reemergence, i.e., no intercommutation. All simulations have a ‘‘sombrero’’ potential V (φ)=λ(‖φ‖2−σ2)2 and a gauge field coupling e. (The numerical results are obtained with λ=0.01, e=0.2, giving the gauge field a slightly longer scale length than that of the scalar field.)

On the cancellation of fermion loops in chiral gauge theories in (1+1) dimensions

We show that for chiral gauge theories in (1+1) dimensions, with the gauge field coupling only to left(right)-handed fermions, the fermion loop contributions cancel in the vacuum expectation value of gauge invariant quantities, if the regularization of the theory respects the left(right)-handed coupling.

Chern-Simons and Wess-Zumino terms in string theory

The recent work of Nepomechie on the coupling of background vector and antisymmetric tensor gauge fields to bosonic strings is interpreted via the geometry of fiber bundles. The role of the Chern-Simons form is clarified. It is part of a Wess-Zumino term in the total space of the bundle.

Chern-Simons terms and Bosonic strings

We discuss the coupling of background chiral vector gauge fields to closed Bose strings. The appearance of Chern-Simons terms in such couplings is elucidated.

Phase structure of scalar compact QED

We give a detailed account of our Monte Carlo investigation of the d = 4, U(1) gauge-Higgs model with Higgs fields in the fundamental representation and with full radial degree of freedom. We found that the phase transition between the Coulomb and the Higgs phases is of first order for small quartic coupling λ and weakens when either λ or the inverse gauge field coupling β increase. A study of the specific heat on the phase transition at λ = 3 and β = 2.5 shows remarkable finite size effects consistent with a second-order phase transition with critical index ν ⋍ 0.56.

Four-dimensional symmetry from a broad viewpoint.

We propose a finite and unitary quantum «elecweakdynamics» with the «SU 2×U 1 structure» which may not have the full gauge symmetry. The Higgs scalar fields are not necessary. Gaugeboson massesM W andM Z can be generated by kinematical symmetry-breaking due to the coupling of vacuum fields and gauge fields. It is a local interaction theory formulated on the basis of i) a new principle of universal probability distributionP(p, m) for field oscillators of all fields and ii) the new four-dimensional symmetry framework of «common relativity». We do not employ the four-dimensional framework of special relativity because it is too restrictive to allow the universal probability principle. This principle introduces a radical lengthR into physics and changes drastically the high-energy behaviour of propagators. It makes the theory finite without upsetting unitarity. We show how scattering cross-sections, static electric potential and particle decay in flight are affected by the universal probability principle. These modifications can be tested experimentally.

Four-dimensional symmetry from a broad viewpoint

We propose a finite and unitary quantum «elecweakdynamics» with the «SU2×U1 structure» which may not have the full gauge symmetry. The Higgs scalar fields are not necessary. Gaugeboson massesMW andMZ can be generated by kinematical symmetry-breaking due to the coupling of vacuum fields and gauge fields. It is a local interaction theory formulated on the basis of i) a new principle of universal probability distributionP(p, m) for field oscillators of all fields and ii) the new four-dimensional symmetry framework of «common relativity». We do not employ the four-dimensional framework of special relativity because it is too restrictive to allow the universal probability principle. This principle introduces a radical lengthR into physics and changes drastically the high-energy behaviour of propagators. It makes the theory finite without upsetting unitarity. We show how scattering cross-sections, static electric potential and particle decay in flight are affected by the universal probability principle. These modifications can be tested experimentally.

Phase structure of U(1) gauge-higgs theory on D = 4 lattices

We describe a rich phase structure observed in Monte Carlo simulations of the d = 4 U(1) gauge-Higgs system on lattices up to size 8 4. The charge-one Higgs field has a dynamical radial degree of freedom. The phase transition between the Coulomb and the Higgs phases is of first order for small values of the quartic coupling γ and weakens when either γ or the inverse gauge field coupling β increase. The confinement-Higgs transition approaches with decreasing γ the two frustrations phases found for β < −1 and might be analogous to a spin-glass transition.

Microcanonical determination of effective-spin models for finite-temperature QCD.

Using microcanonical simulations we determine the dependence of the finite-temperature QCD effective-spin model coupling $J$ on ${g}^{2}$, the gauge-field coupling. The results are compared with the theoretical prediction.

Feynman rules for gauge fields in the presence of a dielectric medium

T. D. Lee's method for developing the Feynman rules for gauge fields in a cavity is reformulated in terms of the path integral. His work is then extended by deriving these rules, in the Feynman gauge, for a spherical cavity. In any gauge only the gauge particle propagator is altered, while all the Feynman rules for gauge field couplings are left unaltered by the presence of a dielectric medium.

Effective theories with broken flavor symmetry

We generalize the work of Ovrut and Schnitzer on effective theories derived from a non-Abelian gauge theory to include the physically interesting case of broken flavor symmetry. Our calculations are performed at the one-loop level. We show that at an intermediate stage in the calculations two distinct renormalized gauge coupling constants appear, one describing gauge field coupling to heavy particles and the other describing coupling to light particles. Appropriately modified Slavnov-Taylor identities are shown to hold. We also consider a simple alternative to the Ovrut-Schnitzer rules for calculating with effective theories.

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4 4 lattice. We compare our results for 〈 S eff〉 and 〈 ψψ〉 for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈 S eff〉 turns out to be quite small for κ⩽ 1 8 .

Three-loop charge renormalization effects due to quartic scalar self-interactions

Dimensionally regularized dispersion theory is used to compute the $O({\ensuremath{\hbar}}^{3}{g}^{3}{f}^{2})$ contribution to the charge renormalization function ${\ensuremath{\beta}}_{g}$, where $g$ is a gauge field coupling and $f$ is a quartic (pseudo) scalar selfcoupling. Some motivations for and systematics of the calculation are discussed. Special attention is given to an $N=4$ globally supersymmetric gauge theory.

Stability analysis for singular non-Abelian magnetic monopoles

The Dirac magnetic monopole potential g A(r) = (g/4π)( r ̂ ×^n )(r− r· n ̂ ) −1 is a stable solution to the Abelian Maxwell equations. The simple generalization A = MA is a solution to the classical non-Abelian generalized Yang-Mills equations, where M is a matrix in the Lie algebra G of the gauge group. In this paper, the stability problem for these non-Abelian monopoles is posed and solved. Although A is essentially Abelian in that A× A = 0 , the stability analysis is non-trivial because it involves the full non-Abelian structure of the theory. It is first shown that the potential A leads to a rotationally invariant classical theory only if the quantization condition g β = 1 2 n β (g β = eigenvalue of M/4π; n β = integer = 0, ±1, ±2,…; 0⩽β⩽ dim G; gauge field coupling constant = e = 1) is satisfied. (In contrast, the Abelian Dirac quantization condition g/4π = 1 2 n is necessary only in quantum mechanics.) The stability analysis is performed by solving the linearized equations for the perturned potentials A(r) + a(r , t) . Thus the existence of a solution a(r ,t) which grows exponentially in time t is equivalent to the instability of A . Using a convenient choice for the basis of G , and the background gauge condition, the equation for the Fourier transform ψ( r,ω) of a is seen to be equivalent to the Schrödinger equation for a particle of unit spin, unit charge and unit anamolous magnetic moment moving in the potential 4πg β A . This equation is separated using the Wu-Yang monopole harmonics, generalized to include unit spin. The radial equation is then solved in terms of the eigenvalues of an operator related to the spin and orbital angular momentum operators. The result is that A is stable if and only if each integer n β is either 0 or ±1. The monopoles with |g β| 1 2 are thus unstable and therefore have no quantum-mechanical significance. This conclusion is used to speculate about the empirical absence of monopoles, the stability of the non-singular ('t Hooft-Polyakov) monopoles, and the existence of magnetic confinement.

Dynamical chiral symmetry breaking in quantum chromodynamics

We examine both dynamical chiral symmetry breaking and explicit breaking due to current quark masses in quantum chromodynamics (QCD). The renormalized current and constituent quark mass are defined. The quark self-energy $\ensuremath{\Sigma}(p)={\ensuremath{\Sigma}}_{D}(p)+{\ensuremath{\Sigma}}_{E}(p)$ has unique contributions from dynamical and explicit symmetry breaking. We determine the asymptotic behavior of ${\ensuremath{\Sigma}}_{D}(p)$ and ${\ensuremath{\Sigma}}_{E}(p)$ as $\ensuremath{-}{p}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$. Although the explicit symmetry breaking dominates in the region controlled by perturbation theory, the dynamical term, which receives contributions from instantons, dominates in the subasymptotic region. The dynamical term is often ignored in the calculations. We also discuss the possibility of a phase transition in QCD for massive quark systems. The structure of the chiral perturbation expansion for light quarks is found to have not only an essential singularity in the gauge-field coupling constant for ${g}^{2}\ensuremath{\le}0$ but also a cut for ${g}^{2}\ensuremath{\le}0$ in amplitudes for which the essential singularity is absent. We also calculate the second-order axial-vector renormalization for a quark with the result ${g}_{A}=1\ensuremath{-}\frac{{g}^{2}}{6{\ensuremath{\pi}}^{2}}$.

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling g(t), t = ln[ F μν a) 2 μ 4 ] . The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F μν a = 0, and ferromagnetism, for which ( F μν a ) 2 = λ 2, i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.