Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.

The unperturbed Hamiltonian of quantum anharmonic oscillator is modified by introducing a simple variational scale parameter. A suitable choice of this parameter makes the eigenvalues rapidly convergent for small size of the determinant in the method of infinite Hill determinant. Simple analytic expressions for the eigenvalues are obtained by matrix diagonalization method.

We consider the quantum mechanics of directly interacting relativistic particles of spin-zero and spin-half. We introduce a scalar product in the vector space of physical states which is finite, positive definite and relativistically invariant and keeps orthogonal eigenstates of total four momentum belonging to different eigenvalues. This allows us to show that the vector space of physical states is, in fact, a Hilbert space. The case of two particles is explicitly considered and the Cauchy problem of physical wave function illustrated. The problem of a spin-1/2 particle interacting with a spin-zero particle is considered and a new equation is proposed for two spin-1/2 particles interacting via the most general form of interaction possible. The restrictions due to Hermiticity, space inversion and time reversal invariance are also considered.

An equation is obtained for the pairing amplitude in a many-electron-proton system at finite temperature. It is noted that under certain approximations it can be solved to give temperature-dependent discrete energy spectra.

Weak electric and magnetic form factors for semileptonic baryon decays are calculated in a relativistic quark model based on the Dirac equation with the independent-quark confining potential of the formV_q(r)=1/2(1+γ⁰)(a²r+V₀). The values obtained for (g₂/g₁) are not very much different from the nonrelativistic results of Donoghue and Holstein. The values of (g₁/f₁) extracted from our model calculations of (f₂/f₁) in the Cabibbo limit compare well with the experimental values. The values of (f₂/f₁) for various semileptonic transitions are also estimated incorporating phenomenologically the effect of nonzerog₂ in the ratio (g₁/f₁). It is found that the SU(3)-symmetry breaking does not generate significant departures in (f₂/f₁) values from the corresponding Cabibbo predictions.

In this short note we wish to point out that the instanton model, which was theoretically fascinating, has recently found application in explaining the hyperfine splitting of mesons and baryons. In particular, the flavour independence ofM_v²-M_P² (i.e. the squared mass difference of the vector and the pseudoscalar mesons), known to be constant for the strange and non-strange mesons in theu,d and the charm quark sectors, have recently been shown to be the same for the beauty sector through experiments. This flavour independence and the magnitude of the splitting agrees remarkably well with the instanton model.

We study the vacuum structure in QCD in a nonperturbative manner using a variational approach with gluon condensates. We show that in Coulomb gauge as the coupling becomes moderately strong, the perturbative vacuum of QCD becomes unstable leading to gluon condensates and a gauge dependent effective mass for the gluons related to the gauge independent value of 〈vac‖G_μν^aG^aμν‖vac〉 of Shifmanet al.

A hadronization model termed as geometric dielectric confinement model is described. The model describes the charmed meson decays quite successfully. In the model we assume that the non-abelian gauge field describing the colour force simulates the effect of a medium having space-dependent dielectric constant. The quarks produced in weak decays move in the dielectric medium such that they are free in limited region of space (r⋍0) and cannot appear as asymptotic states resulting in hadronization. It is found that the dielectric medium resembles anti-desitter microuniverse and the quarks behave essentially as free particles damped by gaussian distribution. The model reproduces from a single Lagrangian the quark motion as well as the form of dielectric function.

We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.

In a low energy Mather-type plasma focus device, hot spots having temperature in the range of few KeV have been observed even 1 µs after the pinch disintegration and in regions away from the pinch area. These hot spots are perhaps created by the thermal runway due to temperature fluctuations in the background gas.