Spinor-inverted solution to thirring model and its generalization to U(n) symmetry

Using the properties of massless free Fermi fields in (1-1) dimensions, it is shown that the spinor inverted form of Klaiber's operator solution to Thirring model is also a scale-invariant solution of the model. But unlike the former it admits a nonvanishing SU(n) current coupling in the generalization of the model to include U(n) symmetry. The value of this coupling constant is fixed and equals Dashen-Frishman number $\text{?4π}\text{(n + 1)}$. The general form of the 2m-point function is given and operates product expansions are exhibited in terms of composite local operators. Scale dimensions of all the bilinear and quadrilinear local operators with U(n) symmetry are computed and are found to depend on n. However, different parts of a composite local operator belonging to different irreducible U(n) representations have the same dimension.     

Band structure in104Ag

The level structure of¹⁰⁴Ag has been studied through the¹⁰³Rh (α, 3nγ) reaction at E_α=40 and 45 MeV. The principal features of the proposed level scheme are in agreement with those obtained earlier through heavy ion reaction. Two quasiparttcle-plus-rotor model calculation has been performed, and the results are compared with experimental data.     

Gauge theory ofSU(2) Weyl fermion: Is it consistent?

Gauge theory ofSU(2) Weyl fermions was alleged by Witten to be inconsistent due to global anomaly. Evidences of inconsistency were also reported from contradictions between the anomalousU(1) symmetry and the fact that theSU(2) group is free of local anomaly. Here we show how the zero modes of Dirac operator, ignored by the authors of these arguments, play a decisive role and saveSU(2) Weyl fermions from inconsistency in each case. The symmetric chiral current, obtained by adding the Chern-Simons current to the fermionic chiral current, fails to be conserved precisely due to the contributions of zero modes to the ABJ anomaly equation. The Jacobian of the fermion measure under rigid chiralU(1) transformation is, however, guaranteed to be trivial by the Atiyah-Singer index theorem. Finally, a zero mode is the point of bifurcation of eigenvalue trajectory in the homotopy space. In its neighbourhood the hypothesis of adiabaticity made by Witten breaks down due to violent oscillations between levels, which makes his allegation of global anomaly untenable.     

Explicit operator solution to thirring model with U(n) symmetry

Two explicit solutions to the Thirring model with U(n) symmetry are constructed following Klaiber's approach. Products of fields are obtained in terms of those for the free case and scale dimensions of composite operators are computed.     

Dependence of the knock-on electron cross-section on muon energy in high,medium and low Z elements

Using the recent experimental results of various authors the dependence of the knock-on electron cross-section on primary muon energy has been studied in detail. It is found that the knock-on production cross-section increases with primary muon energy upto at least 32 GeV in accordance with Bhabha's theory for energy transfers greater than 15 MeV.     

Study of binuclear copper(II) complexes involving bridging Schiff bases—I

Summary The synthesis of binuclear complexes obtained by the reaction of aromatic diamines with the ternary complexes of copper(II) with bis(2-pyridyl)amine (dpa) as primary ligand and salicylaldehyde or 2-hydroxynaphthaldehyde as secondary ligand have been reported. The complexes have been characterized by elemental analyses, conductance, electronic and i.r. spectral studies. Magnetic measurements indicate antiferromagnetic exchange between two copper(II) centres. E.s.r. spectra exhibit a Ms=2 transition, supporting the antiferromagnetic coupling.     

Effect of reducing agent in the formation of CdSe nanoparticles by chemical reduction route

CdSe nanoparticles were synthesized using a simple chemical reduction route at room temperature. Nanoparticle size was controlled by the amount of reducing agent and was characterized by TEM and TED. With increased amounts of sodium borohydride as a reducing agent, the size of the nanoparticles decreased. Size of the nanoparticles varies between 5 and 12 nm with a size dispersion of 1.5 nm. The grown sample was ultra-sonicated in ethanol. The dispersed sample was characterized structurally, optically and electrically. The long-duration photoconductive decay at room temperature shows exponential variation under weak illumination.     

Study of nano-CdS prepared in methanolic solution and polymer electrolyte matrix

This present paper reports the study of cadmium sulphide (CdS) nanoparticles prepared under controlled condition in methanolic solution and also in polyethylene oxide polymer electrolyte matrix. The sulphurations of the cadmium salts were done in situ by a sodium sulphide solution. The concentration of the precursors has been controlled as detailed in the paper. All the preparation and characterization were carried out at room temperature. The nanoparticles were characterized by UV/Vis spectra in the range of 600 to 250 nm. The absence of bulk/micron size particles was noted in either of the system. The absorption edge near 510 nm indicates the presence of bulk CdS, whereas the presence of nanometer-sized particles is also reflected in low wavelength region. The sizes of the particles as well as particle distribution have been estimated using X-ray diffraction and scanning electron microscopy, respectively. A comparison in the spectra has been done for the sample prepared in either of the matrices. The particle size distribution in the polymeric matrix has been found to be more in comparison to that in the methanolic suspension. The polymer is reported to work as a binder, but not as a capping agent.