It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.

Converging lower bound to the critical screening parameterD_c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD_c^ms ≈ [0.764435n⁻²+0.617737n⁻³]⁻¹ wheren is the principal quantum number. The predictedD_c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.

The problem of exponentiation of connected-graph contributionsC, when one carries out only a partial trace of the density matrix of an assembly of bosons in order to construct an effective, low-momentum Hamiltonian, is examined. It is found that besides accounting for the exponentiation of connected graphs, disconnected graphs contribute certain termsD to connected-graph contributions. TheD-terms diminish as the number of iterations increases in the Singh’s renormalization-group theory for the present system. Therefore, these terms play no role in determining critical behaviour of the system.

A heavy quark antiquark potential is suggested connecting asymptotic freedom and quark confinement in a unified way. Theα_g(q²) calculated using Borel summation technique with three loop agrees with the two loopβ-function up tog²/4π≅ 1.1 but changes appreciably afterg²/4π=1.5. The potential so derived satisfactorily explains the $$c\bar c$$and $$b\bar b$$spectrum.

Transport coefficients of quark-gluon plasma are discussed in the framework of relativistic kinetic theory with the relaxation time approximation of Boltzmann transport equation. The expressions for the coefficients of shear and volume viscosities and heat conductivity are derived assuming quark-gluon plasma to be a non-reactive mixture of quarks, anti-quarks and gluons. A lowest order in deviations from local thermal equilibrium and in plasma phase, lowest order in coupling constant are assumed. Entropy production due to irreversible processes is discussed.

Possible occurrence of scaling of differential cross-section for high energy hadronnucleus elastic scattering is demonstrated takingp-⁴He scattering as an example and using three well-known scaling variables proposed earlier for hadron-hadron scattering. The available data on differential cross-section ratio betweenE_lab=45 and 393 GeV are found to scale in all the three variables reasonably well and the positions of the dip and the secondary maximum are found to follow the predicted patterns of behaviour as a function of energy. Extrapolating the fits to the available slope-parameter data onto higher energies and using the scaling curves, the positions of the dip and the secondary maximum and the differential cross-section ratio as a function of |t| are predicted for higher energies.

The differential cross-sections of atomic hydrogen for elastic scattering of electrons and positrons have been rederived with the help of a method using a single parameter-dependent unitary shift operator for the calculation of the direct contribution. When the parameter approaches zerc the new method leads to the well-known conventional Glauber results. The numerical calculations include polarization effects and the exchange corrections obtained according to alternative approximation methods. Results calculated with Franco’s exchange show a definite improvement over the earlier results for medium energy electrons at large angles of scattering. Total elastic cross-sections have been calculated for 50 and 100eV electrons and positrons.

The analysis of the characteristics of a synchronously mode-locked and internally frequency-doubled dye laser is presented. Dependence of dye laser pulse characteristics on the cavity length mismatch of the pump laser and dye laser is studied. Variation of the minimum pulsewidth with intracavity bandwidth and the harmonic conversion efficiency is presented in the form of graphs.

Electron spin resonance studies were carried out on VO²⁺ in cadmium maleate dihydrate single crystals at 303 K. The spin hamiltonian parameters were evaluated. The results lead us to conclude that like Cu²⁺, VO²⁺ enters the lattice interstitially.

The mechanoluminescence (ML) of NaCl, NaBr, NaF, LiCl and LiF crystals ceases at 105, 58, 170, 151 and 175°C respectively. Both the temperatureT_c at whichML disappears and the temperatureT_s required to induce a particular percentage of colouration decay in a given time, decreases with increasing nearest neighbour distance in alkali halide crystals. This perhaps suggests that similar processes cause the disappearance ofml in alkali halide crystals and the colouration decay in their microcrystalline powders. It is shown that mobile dislocations may cause the leakage of surface charge and the decay of colouration in microcrystalline powders.

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth $$\bar \varepsilon \left( {T,\lambda } \right)$$(T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.

The radial distribution function and the equation of state for hard disc fluids have been calculated at various densities by solving Ornstein-Zernike equation using Baxter’s method.