Covariant quantization of string based on BRS invariance

Covariant canonical quantization of the bosonic string is performed, based on the BRS invariance principle. Defining a physical state by a modified form of Kugo-Ojima's subsidiary condition Q_B|phys〉 = 0 (Q_B = BRS charge), we prove a no-ghost theorem in a simple manner. There an interesting relation between critical dimension and BRS symmetry is noticed; namely, the conditions D = 26 and α₀ = 1 for the space-time dimension D and the zero-intercept α₀ of leading trajectory are required by the nilpotency Q_B² = 0 of the BRS charge. In addition, ghost number fractionization is observed in this system.     

Electromigration and permeation of hydrogen and deuterium in silver

A steady state flow technique was used to measure the effective charge number (Z*) and permeability (N) of hydrogen and deuterium in silver. Over the range of temperature (485–720°C) and pressure (220–750 torr) the effective charge number is a constant. The interstitial impurity migrates in the direction of the electron wind with Z_H* = ?6·8 and Z_D* = ? 18. The values of Z* are of the same order as self-electromigration but the size of the isotope effect is surprising. The quantum theories used to explain the isotope effect for hydrogen electromigration in Fe and Ni appear to fail here. In order to determine the effective charge number is was necessary to measure the permeability. For both H₂ and D₂, the permeability in silver follows the equation N = N_O exp(? Q/RT) where N_0D = 2·39 ± 0·40, Q_D = 14400 ± 300, N_OH = 2·86 ± 0·70 and Q_H = 14200 ± 500. Here Q is in units of cal/mol and N is in units of cc(ntp)/(sec - atm² - cm) The isotope effect ratio N_H/N_D = 1·25 was smaller than the classically expected value of (2)^1/2, but could be explained by the theory of Ebisuzaki, Kass and O'Keeffe.     

The mass of the scalar boson beyond the large- N c limit

Within the framework of the 1/N_c expansion of four-fermion interaction models, we analyse the next to leading 1/N_c corrections to the well known large-N _c result M _S = 2M _Q where M _S is the mass of the scalar boson and M _Q is the constituent quark mass. The calculation is performed in the Extended Nambu-Jona Lasinio (ENJL) model which is suitable for describing low energy hadron properties. We treat the model as fully non renormalizable and discuss the comparison with approaches based on the equivalence with renormalizable Yukawa type models. We consider both the G _V = 0 and the G _V ≠ 0 cases with n _f = 2 flavours and study the dependence upon the regularization scheme. We find that pure next-to-leading 1/N _c corrections are large and negative, while a partially resummed treatment can induce positive and smaller corrections. A triplet-singlet states’ splitting is observed.     

Quantum chromodynamics on the mass shell

I prove that in covariant gauges quark and gluon mass-shell renormalization constants obey Ward identities analogous to those of QED: Z₁ = Z₂ and Z₄ = Z₃. This implies that the mixing of ultraviolet and infrared singularities is not a peculiarity of dimensional regularization but a consequence of the Ward identities.     

Die Änderung der Ionenladung von Spaltprodukten bei der Abbremsung in metallischen Absorbern

An experimental set-up is described, which was used to measure the energy and mass as well as the ionic charge of fission products emitted by a Cf²⁵²-spontaneous fission source. The fragments were deflected in a magnetic field of 9700 Oe (Gauss) and were detected by means of two position-sensitive semiconductor detectors. Thin foils of Al, Ni, Ag, and Au were used to investigate the influence of metallic absorber materials on the ionic chargeQ. Within the limits of experimental error it was found thatQ only depends on the velocityv and the atomic numberZ _I of the ions. The relative ionic charge γ=Q/Z _I was found to vary solely withv. The results were compared with those of Moaket al., Almquistet al., Leischner, Opoweret al., and with the theoretical predictions of Bohr. An empirical formula proposed by Leischner was used to fit the experimental data.     

Screening of strongly charged macroparticles in liquid electrolyte solutions

A modified Poisson-Boltzmann model has been proposed which makes it possible to describe the screening of strongly charged macroparticles in liquid electrolyte Z: Z solutions in the case when parameter B= ZeQ₀/εRT?1(Q₀ is the surface electric charge, T is the temperature, ε is the solution permittivity, and Z is the valence of ions) provided that the solution is dilute: κR ≡ (8πZ²e²n_i0/εT)^1/2R?1 (n_i0 is the equilibrium number density of ions). It is assumed that the charge Q₀ of a macroparticle appears as a result of adsorption of ions of a certain polarity on its surface. Quantitative criteria of division of dissolved ions into capable and incapable of adsorption are formulated. For aqueous solutions, the adsorption mechanism always leads to values of B ? 1. It is shown that the charge inversion effect predicted by other authors on the basis of different models must be observed for such solutions for all Z ≥ 1. The effect of Brownian movement of macroparticles on their screening is considered. It is shown that viscous forces emerging during such movement lead to peripheral destruction (“washing out”) of the screening ionic shell of macroparticles and, as a result, to violation of their electroneutrality. This results in the emergence of two types of oppositely charged compound particles with small radii close to R and with radii much larger than R, the charge polarity of the latter being opposite to the polarity of Q₀. It is found that both types of ions of compound particles obey the “law of distribution” of the mean energy of their electric field, expressed by formula (29). The problem of ionic screening of gas bubbles accompanied by the formation of bubstons (bubbles stabilized by ions) is considered separately. It is shown that the bubston radius R in pure water and in aqueous solutions of electrolytes is equal to 14 nm irrespective of the ion number density n_i0. The value of n_i0 determines the number density n _b of bubstons themselves, which are formed spontaneously under equilibrium conditions.     

Geometric quantization in the presence of an electromagnetic field

Some aspects of the formalism of geometric quantization are described emphasizing the role played by the symmetry group of the quantum system which, for the free particle, turns out to be a central extensionG(_m) of the Galilei groupG. The resulting formalism is then applied to the case of a particle interacting with the electromagnetic field, which appears as a necessary modification of the connection 1-form of the quantum bundle when its invariance group is generalized to alocal extension ofG. Finally, the quantization of the electric charge in the presence of a Dirac monopole is also briefly considered.     

无扩散相变中界面动力学的唯象理论及其应用

固态相变中相界面或畴界面的平均运动速度V与有效相变驱动力△G＇(相变驱动力△G与相界面运动阻力△G_R之差)之间的关系可表示为V=φ(△G—△G_R)。当有单向变化的外场(场强为ξ,变化速率为ξ)作用于相变系统并能诱导相界面运动时,就会产生母相/新相间的转变。在相变过程中同时叠加一个交变应力时,则可计算得界面动力学关系V=φ(△G—△G_R)与相变过程内耗Q^-1、相关的模量亏损(△M/M)、相变速率dF/dξ、相变应变ε₀间的关系为 [d lnφ(△G-△G_R)/d(△G-△G_R)]= Q^-1ω/n²M(dF/dξ)ξ = (△M/M)ω/nMε₀(dF/dξ)ξ, 以及 (△M/M)/Q^-1=ε₀/n。此处ω为交变应力的圆频率,M为与振动模式有关的弹性模量,n为应力与界面运动的耦合因子。因此,界面动力学关系式的通解为 V = ∑(±n)/(α≠-1) A_α exp{[(△G-△G_R)/△G_α^*]^{α+ 1}/(α+ 1)} +∑(m)/(β₀) A_β[(△G-△G_R)/△G_β^*]^β 此处n,m为正整数。上式中的各项参数可由实验数据确定。此外,(△M/M)/Q^-1的等式还可用于判别相变过程的模量亏损中有无声子模软化的贡献。 关键词：     

Constrained fermionic system and its equivalence with the free parafermionic theory and nonlinear sigma model

We construct the parafermionic (of orderq) representation of the Kac-Moody and Virasoro algebra and compare it with a constrained fermionic system. We find that the central charge of the Virasoro algebra of the constrained fermionic system depends on the regularization scheme. Using the path integral method, we demonstrate this dependence for theq=2 case and find that it can have the same central charge as the free parafermionic theory or the non-linear sigma model depending on the regularization scheme. We point out some ambiguity in the quantization of the constrained system in Hamiltonian formulation.     

Light thresholds in Grand Unified Theories

In a generic Grand Unified Theory with a relatively small dispersion of the spectrum around the Z-boson and the unification masses, a connection is established, exact at one loop level, between M_Z, G_F, α(M_Z and the strong coupling constant α₃(M_Z. At this level of precision, this avoids the logical and phenomenological inconsistency of predicting α₃(M_Z) by means of the electroweak couplings as extracted from the data in the Standard Model rather than in the complete theory. Attention is paid to the independence of the physical results from regularization and/or renormalization schemes.As a particularly relevant example, the analysis is specialized to the case of the Minimal Supersymmetric Standard Model, with emphasis on light charginos and neutralinos.     

Critical charge in quantum electrodynamics

The critical nuclear charge Z _cr and the critical distance R _cr in the system of two colliding heavy nuclei—they are defined as those at which the ground-state level of the electron spectrum descends to the boundary of the lower continuum, with the result that beyond them (that is, for Z>Z _cr or R<R _cr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Z _cr and R _cr are considered, along with the dependence of these quantities on the screening of the Coulomb field of a nucleus by the electron shell of the atom, on an external magnetic field, on the particle mass and spin, and on some other parameters of relevance. The effective-potential method for the Dirac equation and the application of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z>137 and to the two-body Salpeter equation for the quark-antiquark system are discussed. Some technical details in the procedure for calculating the critical distance R _cr in the relativistic problem of two Coulomb centers are described.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G_M(Q²)/Q_E(Q²) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q² behaviour of the Dirac form factor [1] is also discussed.     

A new method to determine the electroweak couplings of individual light flavours at LEP

A method is presented for determining the yields and properties of individual light quark flavours in Z ⁰ decays that is essentially free of detailed assumptions about hadronisation. The method uses an equation system with the number of events which are single and double tagged by high energy hadrons as inputs. In addition, SU(2) isospin symmetry and the flavour independence of QCD are used to derive general relations between hadron production from the various primary light quarks. Assuming the branching fractions R _q of the Z ⁰ into down and strange quarks to be the same, five million hadronic Z ⁰ decays may allow precisions of δ(R _d = R _s)/(R _d = R _s) ～ 0.05 and δA _FB(d = s) ～ δA _fb(u) ～ 0.015 for the corresponding asymmetries. The method can be extended to include somewhat more model dependent symmetries of hadron production, which then allows the electroweak observables for each of the individual light quarks to be determined.     

Observables and quark confinement in the covariant canonical formalism of Yang-Mills theory

A concise criterion for observables in Yang-Mills theory is presented in the framework of covariant canonical field theory. As an example, the symmetric energy-momentum tensor θ_øν is proved to be an observable and its physically meaningful form is clarified. The validity of the “Maxwell-type” equation of motion is established in the physical subspace $\text{V}$_phys defined by the subsidiary condition $\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{?}\text{phys}\text{〉 = 0}$ (Q_B: BRS charge). Its meaning and consequences are discussed in connection with the notion of observables: especially, all (quasi-) local observables in QCD are shown to be colour singlets and this fact paves the way to quark confinement.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.