The fate of the U(1) goldstone boson

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.     

Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole

The Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed. It is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution: the Fermion propagator has no pole or cut in the time-like region. Discussions of homogeneous and inhomogeneous equations with momentum integration cut-off are also given in some detail.     

Skew-symmetric tensor gauge field theory dynamically realized in the QCD U(1) channel

It is shown that, in order for the U(1) Goldstone boson to decouple from the physical sector, a third rank skew-symmetric tensor gauge field theory has to be realized dynamically by asymptotic fields of bound states in QCD. The abelian-like gauge invariance of this tensor gauge theory is just a realization of the original QCD gauge (BRS) invariance which hence assures the decoupling of all the bound-state modes by the “quarlet mechanism”. A general procedure for fixing gauges in such types of skew-symmetric tensor gauge theories is also presented.     

A multi-wafer growth technique for GaAs vapor phase epitaxy using the AsCl3-Ga-N2 system with a horizontal reactor

A multi-wafer growth technique for vapor phase epitaxial GaAs has been developed using the open-tube AsCl₃-Ga-N₂ system with a conventional horizontal reactor. Use of this technique allows to process 4 wafers in a run with each wafer being 6 cm². The uniformities of growth rate, carrier concentration, and Hall mobility with wafer-to-wafer are typically ∽±3%, ∽±4%, and ∽±3%, respectively, and are shown to be sufficient for demanding microwave device applications.     

Preparation and Dielectric Properties of YMnO3 Ferroelectric Thin Films by the Sol-Gel Method

Thin films of YMnO3 are proposed as a new candidate for non-volatile ferroelectric memory devices. They were prepared via solutions through two different processes: thermal decomposition and reflux using yttrium acetate tetrahydrate and manganese acetate tetrahydrate as starting materials. For coatings prepared by thermal decomposition process, the starting materials were dissolved in ethanol containing diethanolamine, and single phase YMnO3 was obtained with heat-treatment at 900°C. When the starting materials were refluxed using 2-ethoxyethanol as a solvent, single phase YMnO3 was obtained with heat-treatment at 800°C. Scanning electron microscopy showed that the 300 nm thick films with a stoichiometric Y/Mn ratio had many pinholes, and a very large dielectric loss, 0.83 at 100 kHz. Inclusion of 5–10% excess of Y in the coating solution produced dense structures with improved dielectric properties. The dielectric constant and loss tangent of the thin films with Y/Mn ratio of 1.00/0.90 were about 20 and 0.05 at 100 kHz, respectively.     

Characters of Demazure modules and solvable lattice models

We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one-dimensional configurations which we call unrestricted, classically restricted and restricted paths. As an application, characters of Demazure modules are obtained in terms of q-multinomial coefficients for several level-1 modules of classical affine algebras.     

Optical rotatory dispersion studies—CXII thiosteroids (20) An octant rule for the thiocyanate chromophore and its application to rotameric equilibrium studies in the steroid series

Optical rotatory dispersion and circular dichroism measurements of a number of steroidal thiocyanates have demonstrated that a low intensity absorption near 250 nm is optically active. On the assumption that this transition of thiocyanates is qualitatively similar to the n → π^* transition of azides, an octant rule is proposed for thiocyanates, which leads to the prediction of the sign of the Cotton effect. Its potential utility is demonstrated by analyzing rotameric contributions of various steroidal thiocyanates.     

A generalized simple random walk in one dimension related to the Gaussian polynomials

A generalization of the relation between the simple random walk on a regular lattice and the diffusion equation in a continuous space is described. In one dimension we consider a random walk of a walker with exponentially decreasing mobility with respect to time. It has an exact solution of the conditional probability, that is expressed in terms of the Gaussian polynomials, a generalization of binomial coefficients. Taking a suitable continuum limit we obtain the corresponding transport equation from the recursion relation of the discrete random walk process. The kernel of this differential equation is also directly obtained from that conditional probability by the same continuum limit.