Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

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

Squeezed Coherent State Representation of Scalar Field and Particle Production in the Early Universe

The present work is an attempt to explain particle production in the early univese. We argue that nonzero values of the stress-energy tensor evaluated in squeezed vacuum state can be due to particle production and this supports the concept of particle production from zero-point quantum fluctuations. In the present calculation we use the squeezed coherent state introduced by Fan and Xiao [7]. The vacuum expectation values of stressenergy tensor defined prior to any dynamics in the background gravitational field give all information about particle production. Squeezing of the vacuum is achieved by means of the background gravitational field, which plays the role of a parametric amplifier [8]. The present calculation shows that the vacuum expectation value of the energy density and pressure contain terms in addition to the classical zero-point energy terms. The calculation of the particle production probability shows that the probability increases as the squeezing parameter increases, reaches a maximum value, and then decreases.

Squeezed Coherent State Representation of Scalar Field and Particle Production in the Early Universe

The present work is an attempt to explain particle production in the early univese. We argue that nonzero values of the stress-energy tensor evaluated in squeezed vacuum state can be due to particle production and this supports the concept of particle production from zero-point quantum fluctuations. In the present calculation we use the squeezed coherent state introduced by Fan and Xiao [7]. The vacuum expectation values of stressenergy tensor defined prior to any dynamics in the background gravitational field give all information about particle production. Squeezing of the vacuum is achieved by means of the background gravitational field, which plays the role of a parametric amplifier [8]. The present calculation shows that the vacuum expectation value of the energy density and pressure contain terms in addition to the classical zero-point energy terms. The calculation of the particle production probability shows that the probability increases as the squeezing parameter increases, reaches a maximum value, and then decreases.