Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Theory of Breaking of a Potyrner Molecule under Tension

The thesis presents the dynamics of a polymer chain under tension. It includes existing theories of polymer fracture, important theories of reaction rates, the rate using multidimensional transition state theory and apply it to the case of polyethylene etc. The main findings of the study are; the life time of the bond is somewhat sensitive to the potential lead to rather different answers, for a given potential a rough estimate of the rate can be obtained by a simples approximation that considers the dynamics of only the bond that breaks and neglects the coupling to neighboring bonds. Dynamics of neighboring bonds would decrease the rate, but usually not more than by one order of magnitude, for the breaking of polyethylene, quantum effects are important only for temperatures below 150K, the lifetime strongly depends on the strain and as the strain varies over a narrow range, the life varies rapidly from 105 seconds to 10_5 seconds, if we change one unit of the polymer by a foreign atom, say by one sulphure atom, in the main chain itself, by a weaker bond, the rate is found to increase by orders of magnitude etc.

Ultrasonic measurement of the elastic constants of selected nonlinear optical /semiorganic crystals with orthorhombic symmetry

Ultrasonic is a good tool to investigate the elastic properties of crystals. It enables one to determine all the elastic constants, Poisson’s ratios, volume compressibility and bulk modulus of crystals from velocity measurements. It also enables one to demonstrate the anisotropy of elastic properties by plotting sections of the surfaces of phase velocity, slowness, group velocity, Young’s modulus and linear compressibility along the a-b, b-c and a-c planes. They also help one to understand more about phonon amplification and help to interpret various phenomena associated with ultrasonic wave propagation, thermal conductivity, phonon transport etc. Study of nonlinear optical crystals is very important from an application point of view. Hundreds of new NLO materials are synthesized to meet the requirements for various applications. Inorganic, organic and organometallic or semiorganic classes of compounds have been studied for several reasons. Semiorganic compounds have some advantages over their inorganic and inorganic counterparts with regard to their mechanical properties. High damage resistance, high melting point, good transparency and non-hygroscopy are some of the basic requirements for a material to be suitable for device fabrication. New NLO materials are being synthesized and investigation of the mechanical and elastic properties of these crystals is very important to test the suitability of these materials for technological applications