Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

On the challenge of measuring the colour charge of gluons

We propose two ways of measuring “directly” the chromodynamic gluon self-couplings. We argue that the measurements would serve to establish (or disprove) the gauge and non-Abelian nature of the candidate strong-interaction theory: QCD. Both experiments concern the production in e⁺e^? annihilation of a heavy vector meson resonance, followed by its hadronic decay into three “gluon jets”. The asymmetry of the decay plane relative to the electron axis is a measure of $\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{=}\text{g}{}^2\text{4π}$, with g the coupling for gluon self-interactions. If QCD is right, this value of g should coincide with the measured coupling of quarks to gluons. The two proposed experiments are difficult: they both demand very large statistics, one requires longitudinally polarized beams, the other the detection of weak-electromagnetic interferences. But the stakes are high.     

The mass of the muon

It is shown that a classical relativistic charged particle has an anomalous magnetic moment g=4α/3. If such a “dressed” particle with its mass m, charge e, and anomalous magnetic moment g is quantized by a generalized Dirac equation, then the wave equation predicts a second mass m_μ=m_e(3/2α+1). It is suggested that a magnetic portion of the self-energy is quantized.     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

Strings with dimension-dependent intercept

By changing the boundary conditions of the relativistics string in extra dimensions, the intercept α(0) is lowered to $\text{1 ?}\text{1}\text{16}\text{(26 ?D}{}_0\text{)}$ in the modified orbital model, where D₀ is the dimensionality of the Poincaré-invariant subspace of space-time. In the modified model of the spinning string, the boson intercept becomes $\text{1}\text{2}\text{?}\text{1}\text{8}\text{(10 ? D}{}_{\mathrm{o}}\text{)}$, while the fermion intercept stays at zero. The projective invariance of the ground state is broken, giving the “photon” mass by a Higgs-like mechanism. Unfortunately, the strings have a negative “G parity”, so the usual, unshifted strings appear as intermediate states in the scattering amplitudes. Also, some of the amplitudes are not dual.     

Magnetic flux lines as relativistic strings

It is suggested that the relativistic string of the dual resonance model of hadrons is a line of quantised magnetic flux. Accordingly, quarks have magnetic charge. Assuming quarks of magnetic charge ${}^{\mathrm{+}}\text{g,?g}$, baryons are composed of three quarks. States of one, two, four or five quarks will not normally occur.     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

Scaling of the “superstable” fraction of the 2D period-doubling interval

The scaling properties of a “superstable” parameter interval, $\text{C}$, where the eigenvalues about a period-2n orbit are complex, are derived for 2D period-doubling maps. The ratio of $\text{C}$ to the whole parameter interval, between the nth and the (n+1)st bifurcation, is shown to be a universal function of the effective jacobian, B_e, only (B_e≡B²ⁿ, B is thejacobian of th e map). Unlike the whole period-2ⁿ interval, $\text{C}$ has a convergence rate that behaves as $\text{4.6692016×B}{}^{\mathrm{<mtext>-1</mtext><mtext>4</mtext>}}{}_{\mathrm{e}}$ as B_e↓), wh ile its complement has a convergence rate 8.7210972/4 as B_e↑1.     

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.     

Magnetic field dependence of the thermoelectric power of n - type gallium arsenide in the extreme quantum limit

The effect of the quantization of the electron energy levels in a strong transverse magnetic field H on the low-temperature thermoelectric power (TEP) S of a high-purity isotropic semiconductor ($\text{n}$ - type gallium arsenide GaAs) is investigated theoretically. The “electron-diffusion” (S_e) and “phonon-drag” (S_p) components of S( = S_e + S_p) are calculated in the extreme quantum limit, when all the electrons in the conduction band are concentrated in the lowest Landau level. The transition to nondegeneracy, which takes place when the bottom of the lowest Landau level is driven through the Fermi level, has a large effect on the variations of S_e and S_p with magnetic field. The results are illustrated with numerical calculations for $\text{n}$ - type GaAs at 4.2 K with 1.2 × 10¹⁶ cm^-3 electrons.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

Collective states in 48V

The low-lying positive parity states of ⁴⁸V have been studied in the framework of deformed configuration mixing model calculations based on projected Hartree-Fock theory, within the full fp shell space. The modified Kuo-Brown effective interaction has been used. The calculated spectrum and the electromagnetic properties of these states are in good agreement with the experiment. The calculation predicts an excited low-lying collective K = 2⁺ band in the spectrum of ⁴⁸V and accounts for the observed breakdown of the “signature” selection rule arising in the shell-model calculation within the ($\text{f}\text{7}\text{2}\text{)}{}^{\mathrm{nd}}$ space. It does not favour a 5⁺ assignment to the observed 1.099 MeV level. Two sets of proton and neutron effective charges (i) e_p = 1.32e and e_n = 0.89e and (ii) Kuo and Osnes charges e_p = 1.25e and e_n = 0.47e were employed. The observed decay properties appear to favour the latter charges. Our model also explains in a semiquantitative way the observed K-value, moment of inertia parameter and the intrinsic quadrupole moment of the K = 1^?1 rotational band.     

Theoretical studies of chemisorbed oxygen on Ag(110)

The interaction of an oxygen atom with a 26-atom cluster model of the (110) face of Ag has been investigated with ab initio self-consistent-field and configuration-interaction theory. The SCF results for the bridge site (C_2v) predict $\text{r = 0.3}\text{A}\text{?}$ and ω_e = 327 cm^?1, in good agreement with the available experimental evidence. The calculated binding energy (D_e = 9 kcal/mole) is roughly an order of magnitude too small. The inclusion of electron correlation increases r_e and ω_e only slightly, but should have a dramatic effect on D_e. The ground state corresponds to a “surface oxide” state. The theoretical projected density-of-states curves exhibit “bonding” and “anti-bonding” O(2p) peaks, separated by ~ 6 eV, in good agreement with recent angle-resolved photoemission data.     

The 2880-Å emission spectrum of I2: Ion-pair states near 47 000 cm−1

An emission system of I₂ in Ar in the region 2830–2890 Å is examined under high resolution and found to display fine violet-degraded band structure. This system is interpreted as a charge-transfer transition originating from an ion-pair state near 47 000 cm^?1 and terminating on a weakly bound state which dissociates to two ground-state atoms. This interpretation is supported by spectral simulations employing a bound-free model. The transition is tentatively assigned as $\text{0}{}_{\mathrm{<mtext>g</mtext>}}{}^{\mathrm{?}}\text{→ 2431 0}{}_{\mathrm{<mtext>u</mtext>}}{}^{\mathrm{?}}\text{(}{}^3\text{Π}\text{)}$, according to which the excited state becomes the fourth ion-pair state near 47 000 cm^?1 to be experimentally characterized, and the lower state is the last component of the lowest ³Π state to be identified. The vibrational assignments include about 45 bands in ¹²⁷I₂ and ¹²⁹I₂, spanning v′ = 0–4 and v″ = 6–19, but with the numbering of the lower state remaining uncertain by several units. The main spectroscopic constants for the excited state are T_e = 47 070 cm^?1, ?_e = 105.7 cm^?1, ?_ex_e = 0.49 cm^?1. The spectral simulations place the lower state's potential curve 34 650 cm^?1 below the upper state at R = R′_e, with slope ?850 cm^?1/Å. For our “best” numbering of the lower state, ?_e = 20.5 cm^?1, ?_ex_e = 0.29 cm^?1, T_e = 12 190 cm^?1, and D_e = 360 cm^?1.     

Derivation of relativistic charge-monopole and monopole-monopole potentials from field theory

Relativistic potentials (generalizing the Breit-potential of quantum electrodynamics) between spin $\text{1}\text{2}\text{-}\text{electric}$ and magnetic charges are presented, each monopole g_j having its own singularity-string along some direction n_j. The monopole potentials involve integrations along the singularities. By using suitable gauge transformations and limiting procedures a simple form of the potential independent of n_j is derived, if the string connects two monopoles.     

An identity for T-ordered exponentials with applications to quantum mechanics

The solution of the Cauchy problem for Liouville's equation φ_xy = e^φ is shown to be equivalent to the calculation of a T-ordered exponential of a two-dimensional variable matrix. This gives rise to an identity for the T-ordered exponential involving two arbitrary functions. The formalism is applied to the time evolution of a magnetic dipole in a time dependent magnetic field and to the one-dimensional Dirac equation with external potential $\text{V(x) = (n +}\text{1}\text{2}\text{)λ}$ tanh λx which is relevant for field theoretic applications. A generalization to n-dimensional matrices is also given.     

Chiral symmetry breakdown,anomaly, and the PCAC relation on a lattice

Lattice fermion formulation is investigated using a solvable model which resembles quantum chromodynamics. CP₂^N?1 models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the $\text{1}\text{N}$ expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) apparently occurs in this model, and the “pion” mass is calculated. From the above results, it is shown that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.     

Anomalous phonon intensities in the Raman spectrum of disordered CsMg1−xCoxCl3

The five Raman-active $\text{k}\text{= 0}$ phonons have been measured at low temperatures and for a range of x in the disordered lattice CsMg_1-xCo_xCl₃. While the E_2g^a, E_2g^b, E_2g^c and A_1g modes at 55.0, 132.0, 189.0 and 255.0 cm^?1 for x = 0 exhibit normal one-mode behaviour, the intensity of the E_1g phonon at 127.5 cm^?1 has a most unusual concentration dependence which requires a new theory.