The problem of confinement: From two to four dimensions

The Coulomb law of “electrodynamics” in two space time dimensions in extended to four dimensions. The result is that antisymmetric tensor potentials A_μν? subject to the gauge transformation δA_μν? = ?_μΛ_ν? + ?_?Λ_?μ + ?_?Λ_μν can be effectively used as confining potentials.     

Quantum inequivalence of different field representations

The gauge theories of antisymmetric tensor potentials A_μν and A_μν? describe 1 and 0 degrees of freedom, respectively. Yet we show the gravitational trace anomalies of A_μν and a scalar field A to be different, and that of A_μν? to be non-vanishing. Corresponding inequivalences also occur in their one-loop counterterms when the spacetime has non-trivial topology. Furthermore, the coupling of A_μν? to gravity provides a gauge principle derivation of the cosmological constant. Possible applications to supergravity are also discussed.     

Generalizing some properties of short range classical solutions to Yang-Mills theory

We extend a theorem which states that for classical solutions of Yang-Mills theory, the field G_μν has to decrease at least as fast as the source S_μ at spatial infinity, provided G_μν decreases exponentially [G_μν ～ exp(?Mr)]. This generalization encompasses all decreases G_μν ～ exp(?Mr^η) with η > 0, r→∞. This is done by assuming an integral representation for A_μ, the vector potential, and imposing some regularity conditions on A_μ, valid as r→∞.     

Hard pions and axial meson exchange current effects in negative muon capture in deuterium

The contribution of the axial meson exchange current effects to the doublet transition rate in the reaction μ^? +d → 2n+ ν_μ is calculated by using the minimal, chiral and approximately gauge invariant Lagrangian model for the A₁ρπ system. The contribution from the ρ-π weak decay process current usually considered is found to be nearly cancelled by that from the A₁ pole graph which is prescribed by the underlying invariance principles. Correct treatment of the N¹ propagator in the N¹ excitation current of the pion range leads to ≈ 30 % suppression of the N¹ effect.     

Renormalizability and asymptotic freedom in quantum gravity

We discuss a previously proposed renormalizable theory of gravity involving R²_μν, and N massless fermion (vector boson) fields in which the unitarity problem is resolved within a $\text{1}\text{N}$ expansion. The infrared limit is precisely Einstein's theory, but the high-energy behavior is determined by the dimensionless, asymptotically free coupling of the R²_μν. Various attractive possible consequences of the theory are pointed out.     

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B_μν subject to the gauge transformation δB_μν = ?_μξ_ν ? ?_νξ_μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.     

New high negative dispersion photonic crystal fiber

A new high negative dispersion photonic crystal fiber is proposed. It has double-core structure. The inner core has a circle germanium-doped region. The outer core is formed by removing the 3rd ring air-holes around the core. There are two ring air-holes between the two cores, Diameter of the 1st ring air holes is bigger than that of the 2nd ring air-holes, this can make mode coupling between inner mode and outer mode and showed that the high negative PCF is the result of this structure characteristics. There are honeycomb photonic lattice in the PCF's cladding. The influence of the structure parameters deviated from the design those on the chromatic dispersion are evaluated. When the structure parameters Λ=1.50 μm, d_core=2.10 μm, d₁=0.90 μm, d₂=0.44 μm and d₃=1.04 μm, the dispersion coefficient D is −1320 ps/(nm·km) at 1550 nm. This is a new kind of chromatic dispersion compensation PCF.     

The microwave spectrum of trans 1-nitropropene

Rotational transitions of 1-nitropropene arising from the ground vibrational state and from three excited states of the nitro torsional vibration have been assigned. The values of the rotational constants in MHz are: A₀=10 650B₀=2028.56C₀1722.16A₁10 615 B₁=2028.47 C₁=1725.11 A₂10 570 B₂ 2028.31 C₂= 1727.32 A₃= 10 512 B₃2028.11 C₃=1729.37The dipole moment components are μ_a = 4.52 D, μ_b = 0.42 D and μ_total = 4.54 D. From the lack of observable internal rotation splittings the barrier to internal rotation of the methyl group is shown to be greater than 2250 cal/mole.     

Commitment Versus Persuasion in the Three-Party Constrained Voter Model

In the framework of the three-party constrained voter model, where voters of two radical parties (A and B) interact with “centrists” (C and C _ζ ), we study the competition between a persuasive majority and a committed minority. In this model, A’s and B’s are incompatible voters that can convince centrists or be swayed by them. Here, radical voters are more persuasive than centrists, whose sub-population comprises susceptible agents C and a fraction ζ of centrist zealots C _ζ . Whereas C’s may adopt the opinions A and B with respective rates 1+δ _A and 1+δ _B (with δ _A ≥δ _B >0), C _ζ ’s are committed individuals that always remain centrists. Furthermore, A and B voters can become (susceptible) centrists C with a rate 1. The resulting competition between commitment and persuasion is studied in the mean field limit and for a finite population on a complete graph. At mean field level, there is a continuous transition from a coexistence phase when ζ<Δ _c =δ _A /(1+δ _A ) to a phase where centrism prevails when ζ≥Δ _c . In a finite population of size N, demographic fluctuations lead to centrism consensus and the dynamics is characterized by the mean consensus time τ. Because of the competition between commitment and persuasion, here consensus is reached much slower (ζ<Δ _c ) or faster (ζ≥Δ _c ) than in the absence of zealots (when τ～N). In fact, when ζ<Δ _c and there is an initial minority of centrists, the mean consensus time grows as τ～N ^?1/2 e ^Nγ , with N?1 and . The dynamics is thus characterized by a metastable state where the most persuasive voters and centrists coexist when δ _A >δ _B , whereas all species coexist when δ _A =δ _B . When ζ≥Δ _c and the initial density of centrists is low, one finds τ～lnN (when N?1). Our analytical findings are corroborated by stochastic simulations.     

ω Meson photoproduction from deuterium at 3.9 GeV photon energy

Measurements are presented of the cross sections for ω meson photoproduction from deuterium at an average photon energy of 3.9 GeV. The cross section for the coherent process γd → dω is found to be 1.4 ± 0.5 μb and that for the incoherent process γd → npω is 3.3 ± 0.7 μb. The forward differential cross section for γd → dω is estimated to be (dσ/dt)_t=0 = 54 ± 20 μb/GeV². This result indicates that the value of the A₂ exchange amplitude in ω photoproduction from hydrogen is less than that predicted from the measurements of the difference between the total hadron photoproduction cross sections from neutrons and protons. We note that the world data tend to show that the A₂ exchange amplitude is more consistent with zero than with the value needed to explain these differences. Measurements are also presented of the ratio of the coupling constants of the photon to the ? and ω mesons which tend to favour the vector dominance model proposed by Das, Mathur and Okubo with exact SU(3) symmetry at infinite energies.     

Lyapunov Exponents for Products of Complex Gaussian Random Matrices

The exact value of the Lyapunov exponents for the random matrix product P _N =A _N A _N?1?A ₁ with each $A_{i} = \varSigma^{1/2} G_{i}^{\mathrm{c}}$ , where Σ is a fixed d×d positive definite matrix and $G_{i}^{\mathrm{c}}$ a d×d complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

Interacting instantons, 1N expansion and the gluon condensate

Based on the dilute gas approximation (DGA) with repulsive and dipole interactions we discuss the N dependence of the vacuum energy density, 〈α_SF_μν^aF_μν^a〉 and of the topological charge correlation function at the crossover point of the instanton driven β function with the strong coupling one.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_μν. After having obtained the expression of the local spin-dependent phase-space density f(x, p)_στ in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_μν constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω_μνσ^μν. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^μ = σ_μνu^ν ≠ 0, in contrast to the common assumption t^μ = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.     

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.     

Nuclear magnetic resonance on oriented 11/2− 129mXe and131mXe in Fe

The magnetic hyperfine splitting frequenciesν _M=¦gμ _NB_HF/h.¦ of the 11/2^? isomeric states^129m Xe (T_1/2=8.9d) and^131mXe (T_1/2=11.8d) in Fe were measured with nuclear magnetic resonance on oriented nuclei at temperatures of 10–15 mK as 188.0(1) MHz and 209.8(1) MHz, respectively, the samples being prepared with the technique of recoil implantation after (α, x n) reactions. The magnetic moments of^129m Xe and^131m Xe are deduced to be (?)0.8914(6)μ _N and (?)0.9943(6)μ _N, respectively. The missing γ-anisotropies for allγ-transitions following the decay of 36.4d ¹²⁷Xe indicateI=1/2 for the ground state spin of¹²⁷Xe.     

The heterotic string and supersymmetric counterparts of the Lorentz Chern-Simons terms

The heterotic string three-point amplitude, which involves two fermionic and one bosonic state, determines some of the terms that must be added to the action of the N=1 supergravity coupled to N=1 supersymmetric Yang-Mills in ten dimensions to preserve supersymmetry, if the Lorentz Chern-Simons term is included in the definition of the field strength H_μνϱ for the cancellation of anomalies. Our calculation reveals an interesting structure, which suggests that the relevant H-Bianchi for the analysis of possible heterotic string compactifications involves a spin connection possibly with torsion.     

Comparative study of large-solid-core photonic crystal fibers: Dispersion and effective mode area

In this study, large-solid-core photonic crystal fibers with fixed air-hole diameter d = 0.84 μm and with fixed pitch length Λ = 4.2 μm are investigated for different d/Λ ratios. The dispersions and the effective mode-areas are obtained and compared for both the structures. It is seen that the dispersion management is easier by using the fixed d structures, but for working around the same zero dispersion points in a large interval of d/Λ the fixed Λ structures are more available. The A_eff values larger than 100 μm² are obtained with d/Λ smaller than 0.2 for both the two structures. A_eff increases rapidly with decreasing d/Λ to 0.1 and then reaches to A_eff value of 500 μm² at the d/Λ = 0.1 for the fixed d structures. The single-mode regime for the two structures is also discussed.     

An investigation of theL 2-L 3 Coster-Kronig transition probability for 63≦Z≦96

Nuclear spin polarization in the 4f ¹⁴6s ^{2 1} S ₀ ground state of¹⁷⁵Lu⁺(I=7/2) ions is achieved by optical pumping with the resonance line (¹ S ₀-¹ P ₁,λ=261.5 nm). Nuclear magnetic resonance of the free ions in He buffer gas yields for the magnetic dipole momentμ(¹⁷⁵Lu)=2.2240(11)μ _n (with diamagnetic correction). This value can be used for a more accurate determination of the magnetic dipole moments of other Lu isotopes from knownA factor ratios. A comparison with nuclear induction measurements in solids results in the chemical shiftsδ(LuB₁₂)=?23(5)·10^?4 andδ(LuSb)= ?31(5)·10^?4.