The nonperturbative propagator and vertex in massless quenched QED_d

It is well known how multiplicative renormalizability of the fermion propagator, through its Schwinger-Dyson equation, imposes restrictions on the 3-point fermion-boson vertex in massless quenched quantum electrodynamics in 4-dimensions (QED$_4$). Moreover, perturbation theory serves as an excellent guide for possible nonperturbative constructions of Green functions. We extend these ideas to arbitrary dimensions $d$. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in $d$-dimensions and it naturally leads to a constraint on the fermion-boson vertex. We verify that this constraint is satisfied in perturbation theory at the one loop level in 3-dimensions. Based upon one loop perturbative calculation of the vertex, we find additional restrictions on its possible nonperturbative forms in arbitrary dimensions.Comment: 13 pages, no figures, latex (uses IOP style files

A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models

We study Schwinger-Dyson equation for fermions in Yukawa and Wess-Zumino models, in terms of dynamical mass generation and the wavefunction renormalization function. In the Yukawa model with $\gamma_5$-type interaction between scalars and fermions, we find a critical coupling in the quenched approximation above which fermions acquire dynamical mass. This is shown to be true beyond the bare 3-point vertex approximation. In the Wess-Zumino model, there is a neat cancellation of terms leading to no dynamical mass for fermions. We comment on the conditions under which these results are general beyond the rainbow approximation and also on the ones under which supersymmetry is preserved and the scalars as well do not acquire mass. The results are in accordance with the non-renormalization theorem at least to order $\alpha$ in perturbation theory. In both the models, we also evaluate the wavefunction renormalization function, analytically in the neighbourhood of the critical coupling and numerically, away from it.Comment: 12 pages and 7 Postscript figures, accepted for publication in Journal of Physics G: Nuclear and Particle Physic

Mid-infrared intersubband absorption from p-Ge quantum wells grown on Si substrates

Mid-infrared intersubband absorption from p-Ge quantum wells with Si0.5Ge0.5 barriers grown on a Si substrate is demonstrated from 6 to 9 μm wavelength at room temperature and can be tuned by adjusting the quantum well thickness. Fourier transform infra-red transmission and photoluminescence measurements demonstrate clear absorption peaks corresponding to intersubband transitions among confined hole states. The work indicates an approach that will allow quantum well intersubband photodetectors to be realized on Si substrates in the important atmospheric transmission window of 8–13 μm

Mid-Infrared Intersubband Absorption from P-Ge Quantum Wells on Si

Mid-infrared intersubband absorption from p-Ge quantum wells with Si0.5Ge0.5 barriers grown on a Si substrate is demonstrated from 6 to 9 μm wavelength at room temperature and can be tuned by adjusting the quantum well thickness. Fourier transform infra-red spectroscopy measurements demonstrate clear absorption peaks corresponding to intersubband transitions among confined hole states. The work indicates an approach that will allow quantum well intersubband photodetectors to be realized on Si substrates in the important atmospheric transmission window of 8–13 μm

Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation

Based on the path integral formalism, we rederive and extend the transverse Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger-Dyson equation in which the the transverse Ward-Takahashi identity together with the usual (longitudinal) Ward-Takahashi identity are applied to specify the fermion-boson vertex function. Especially, in two dimensional Abelian gauge theory, we show that this scheme leads to the exact and closed Schwinger-Dyson equation for the fermion propagator in the chiral limit (when the bare fermion mass is zero) and that the Schwinger-Dyson equation can be exactly solved.Comment: 22 pages, latex, no figure

Constraint on the QED Vertex from the Mass Anomalous Dimension γm=1\gamma_m = 1

We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show that it is possible to construct a vertex which not only ensures that the fermion propagator is multiplicatively renormalizable, obeys the appropriate Ward-Takahashi identity, reproduces perturbation theory for weak couplings and guarantees that the critical coupling at which the mass is dynamically generated is gauge independent but also makes sure that the value for the anomalous dimension for the mass function is strictly 1, as Holdom and Mahanta have proposed.Comment: 8 pages, LaTeX, October 199

Gauge Dependence of Mass and Condensate in Chirally Asymmetric Phase of Quenched QED3

We study three dimensional quenched Quantum Electrodynamics in the bare vertex approximation. We investigate the gauge dependence of the dynamically generated Euclidean mass of the fermion and the chiral condensate for a wide range of values of the covariant gauge parameter $\xi$. We find that (i) away from $\xi=0$, gauge dependence of the said quantities is considerably reduced without resorting to sophisticated vertex {\em ansatze}, (ii) wavefunction renormalization plays an important role in restoring gauge invariance and (iii) the Ward-Green-Takahashi identity seems to increase the gauge dependence when used in conjunction with some simplifying assumptions. In the Landau gauge, we also verify that our results are in agreement with those based upon dimensional regularization scheme within the numerical accuracy available.Comment: 14 pages, 11 figures, uses revte

Electromagnetic Form Factors and Charge Radii of Pseudoscalar and Scalar Mesons: A Comprehensive Contact Interaction Analysis

We carry out a comprehensive survey of electromagnetic form factors of all light, heavy and heavy-light ground-state pseudoscalar and scalar mesons. Our analysis is based upon a Schwinger-Dyson equations treatment of a vector $\times$ vector contact interaction. It incorporates confinement and ensures axial vector and vector Ward-Takahashi identities are satisfied along with the corresponding corollaries such as the Goldberger-Treiman relations. The algebraic simplicity of the model allows us to compute the form factors at arbitrarily large virtualities of the probing photon momentum squared with relative ease. Wherever possible and insightful, we compare our results for the electromagnetic form factors and the charge radii with those obtained earlier through Schwinger-Dyson equations, lattice and with experimental observations available. We also comment on the scope and shortcomings of the model.Comment: 13 pages, 13 figure

Synthesis, characterization and ab initio study of WO3 nanocubes with peculiar electrochemical properties

Simple sol–gel method has been exploited to deposit Sn-doped TiO2 thin flms on glass substrates. The resultant coatings were characterized by X-ray difraction (XRD), UV–visible techniques (UV–Vis), Fourier transform infrared spectroscopy (FTIR), and photoluminescence analysis (PL). The XRD pattern reveals an increase in crystallite size of the prepared samples with the increasing doping concentration. A decrease in doping concentrating resulted in the decrease in bandgap values. The diferent chemical bonds on these flms were identifed from their FTIR spectra. The photoluminescence analysis shows an increase in the emission peak intensity with increasing dopant concentration, and this can be attributed to the efect created due to surface states. The prepared samples were tested as antibacterial agent toward both Gram-positive and Gram-negative bacteria like S.aureus (Staphylococcus aureus) and E.coli (Escherichia coli), respectively. The size of the inhibition zones indicates that the sample shows maximum inhibitory property toward E.coli when compared to S.aureus

A microflow electrolysis cell for laboratory synthesis on the multigram scale

A large microflow electrolysis cell for laboratory synthesis on a multigram scale is described. It is based on two circular electrodes with a diameter of 149 mm and a spiral electrolyte flow channel 2000 mm long, 5 mm wide, and 0.5 mm interelectrode gap. Using the methoxylation of N-formylpyrrolidine as a model reaction, it is demonstrated that the cell approaches 100% conversion in a single pass, and it is possible to achieve a reaction selectivity >95% and a product formation rate of >20 g h–1