A scheme of parametrization ofππ S andP partial wave amplitudes is proposed. Analytic, crossing and unitarity properties are rigorously satisfied. The analyticity property is made explicit by the use of a conformally mapped variable. Our expressions fit excellently with both phase shift and inelastic curves for centre of mass energy up to 1·4 GeV.

Assuming that field theoretic Green’s functions scale, expressions for correlation function, number density, pressure are obtained for a relativistic statistical many-body system. The scaling parameter is related to anomalous dimension and is a measure of interaction. The effect of this interaction on the critical mass of dwarf stars is studied and is not found to be insignificant. A mass radius relation is deduced. The Chandrasekhar limit is reproduced in the limit of non-interaction.

A novel approach to energy dependent phase shift analysis ofππ scattering is proposed. Optimised polynomial expansions of Roskies’ amplitudes are given. The parameters of these expansions are searched out by making a fit to the differential cross-sections. Then the transformation matrix between Roskies’ amplitudes and the conventional partial waves is used to compute the phase shifts and inelasticities. Significant improvement is observed in so far as the number of free parameters for a fixed energy phase shift analysis is concerned. Value for the effective Chew-Mandelstam coupling constant, λ_CM, is also estimated.

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.

An elegant analytic method is presented to derive a modified form of the Ornstein-Zernike equation which not only solves the statistical mechanical problem for hard rods and spheres but can be used to find solutions for arbitrary non-vanishing direct correlation functions.

Velocity and attenuation of ultrasonic waves have been measured in complex binary mixtures of benzene and multicomponent coconut oil near the critical temperature in the low MHz region. The experimental results are analysed in terms of theories developed by Kawasaki and Mistura. The characteristic frequency and amplitude parameter determined by fitting the data in the relations proposed by Kawasaki-Mistura are scaled at reduced temperature and these agree with scaling exponents. A small velocity dispersion is also observed.

Ultrasonic propagation in a system consisting of coconut oil and carbon tetrachloride has been considered as a function of temperature nearTc in the low MHz region. A small velocity dispersion is seen in the system. The experimental results have been analysed with recent theories developed by Ferrell and Bhattacharjee. The data on attenuation per wavelength nearTc agree with the scaling relation developed by Kroll and Ruhland.

The structure function of simple monatomic liquids like neon and argon is studied in an approximation scheme where intermediate functionQ(r) is extended beyond hardcore diameter rather than the direct correlation functionC(r). The calculated values show good agreement with experimental values.

A novel method of phase shift analysis for the scattering of charged pion from⁴He nuclei is proposed. The nuclear amplitudef_N(ϑ) has been parametrized in terms of a polynomial expansion in a conformally mapped variable, which is obtained by optimally exploiting the analytic property off_N. The method exhibits a significant reduction in the number of free parameters required for the fixed energy phase shift analysis of the differential cross-section data. The nuclear amplitude thus constructed is then used to obtain phase shifts and inelastic parameters of all possible orders. Reliable values of the real and imaginary parts of the forward amplitude are also obtained.

Contributions to the vacuum polarisation inQCD are calculated separately with fermion as well as boson loops to have an idea of results expected for possible supersymmetric extension. It is found that the results are not altered in any significant way.

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.

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.

A relatively stable method of phase shift analysis of hyperon-nucleon scattering proposed by us is applied to Σ⁺p and Λp scattering. The analytic cutt-planes of analyticity of the helicity amplitudes are mapped into the interior of unifocal ellipses. The helicity amplitudes are then expressed as accelerated convergent expansions in the mapped variable. A definite economy is observed in the number of free parameters for fixed energy phase shift analysis of Σ⁺p and Λp scattering at 40 and 100 MeV and 100 MeV respectively. Twenty six more phase shifts and coupling parameters corresponding to higherJ values are also predicted.

A supersymmetric version of the left right symmetric partial unification group SU_C(4) × SU_L(2) × SU_R(2) is presented. The spontaneous breakdown of gauge symmetry in a favourable chain of descent has been studied in detail. The mass spectra have been calculated. The method of O’Raifeartaigh has been used to break supersymmetry. The lifting of degeneracy of mass levels between physical multiplets has been shown to occur due to radiative corrections.