This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity. It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions. It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.

This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

The chapters in this book deal with: Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic field. The reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion group. The Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limit. It will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example: The design of quantum unitary gates using supersymmetric actions Bosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculus Superstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding it Simplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introduced All through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.

This book covers a variety of problems, and offers solutions to some, in: Statistical state and parameter estimation in nonlinear stochastic dynamical system in both the classical and quantum scenarios Propagation of electromagnetic waves in a plasma as described by the Boltzmann Kinetic Transport Equation Classical and Quantum General Relativity It will be of use to Engineering undergraduate students interested in analysing the motion of robots subject to random perturbation, and also to research scientists working in Quantum Filtering.

This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail. The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan's Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory. The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.

This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years. It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This is a reference book for researchers working in the field of general relativity, quantum mechanics and quantum gravity. A major part of the book deals with the formulation of special relativistic mechanics, special relativistic fluid dynamics and its generalization to general relativity where the gravitational field is described by a metric tensor. Emphasis is laid on the fact that the general theory of relativity is of tensorial character under all dieomorphisms of space-time and hence its field equations, namely the Einstein field equations for gravitation, the Maxwell equations in a curved space-time geometry and the fluid dynamical equations in curved space time are all valid for all observers in the universe. The emphasis throughout is on the fact that matter generates a gravitational field described by a metric that has a non-vanishing curvature tensor and hence such space-times are inherently curved, ie, cannot be transformed into Minkowsian form. There is a final section on quantum mechanics and quantum field theory which introduces supersymmetry and quantum gravity to the reader. The reader after going through this book will be sufficiently well equipped to start research in quantum gravity, i.e, background independent physics which is as yet an unsolved problem owing to renormalization problems. Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This book is about several questions regarding how to describe the quantization of the current density in an antenna and about the nature of the quantum electromagnetic field produced by such a quantum current density. The second quantized current density can be built out of the Dirac field of electrons and positrons while the free electromagnetic or photon field is built out of solutions to the wave equation with coefficients being operators, namely the creation and annihilation operators of the photons. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This book covers all aspects of waves and optics ranging from one dimensional waves in a vibrating string, two dimensional waves in a vibrating membrane, both of which are transverse, three dimensional electromagnetic waves generated by radiating antennas and longitudinal sound/pressure waves in an air column. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information Theory It will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infinite-dimensional operator theory, perturbation theory, stochastic differential equations, and Riemannian geometry. These mathematical tools have been applied to study problems in mechanics, fluid dynamics, quantum mechanics and quantum field theory, nonlinear dynamical systems, general relativity, cosmology, and electrodynamics. A particularly interesting topic of research interest developed in this book is the design of quantum unitary gates of large size using the Feynman diagrammatic approach to quantum field theory. Through this book, the reader will be able to observe how basic physics can revolutionize technology and also how diverse branches of mathematical physics like large deviation theory, quantum field theory, general relativity, and electrodynamics have many common issues that provide the starting point for unifying the whole of physics, namely in the formulation of Grand Unified Theories (GUTS).

This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infinite-dimensional operator theory, perturbation theory, stochastic differential equations, and Riemannian geometry. These mathematical tools have been applied to study problems in mechanics, fluid dynamics, quantum mechanics and quantum field theory, nonlinear dynamical systems, general relativity, cosmology, and electrodynamics. A particularly interesting topic of research interest developed in this book is the design of quantum unitary gates of large size using the Feynman diagrammatic approach to quantum field theory. Through this book, the reader will be able to observe how basic physics can revolutionize technology and also how diverse branches of mathematical physics like large deviation theory, quantum field theory, general relativity, and electrodynamics have many common issues that provide the starting point for unifying the whole of physics, namely in the formulation of Grand Unified Theories (GUTS).

This book covers resonating modes inside device and gives insights into antenna design, impedance and radiation patterns. It discusses how higher-order modes generation and control impact bandwidth and antenna gain. The text covers new approaches in antenna design by investigation hybrid modes, H_Z and E_Z fields available simultaneously, and analysis and modelling on modes with practical applications in antenna design. The book will be prove useful to students, researchers and professionals alike.

This book is on the nonlinear random medium analysis that includes subtopics of terahertz imaging, inverse scattering, plasmonics, quantum optics/communication laser modes, and terahertz photonic antennas. Here in this book, a mathematical framework is developed to analyze the impact of dimensions and chemical potential on nano-antenna channels.

MAGNETO HYDRODYNAMIC ANTENNA: Design and Applications discusses mathematical solutions of rectangular waveguide modes in homogeneous medium, Estimating inhomogeneous dielectric in a rectangular waveguide by classical method, Mathematical solution of resonant modes in cylindrical waveguides, MHD antenna analysis by cavity resonator method, Introduction to magneto hydrodynamics system, Mathematical solution of smart MHD antenna excited at the centre, Two dimensional solution of cylindrical MHD antenna, Design of reconfigurable MHD antenna, Analysis of stacked cylindrical MHD antenna, Discrete solutions of fluid frame MHD antenna with anechoic chamber measurements, Analysis of nonlinear permittivity using Kronecker Tensor, Superstrate based high gain antenna and Design of concentric cylindrical resonator antenna. The book includes Annexures with basic design formulations and Case studies based on implemented MHD antennas.

The mathematical tools used in signal analysis involve differential and difference equations, integral equations, matrix algebra and calculus, complex analysis and probability theory and random processes. This book applies these tools to problems in various branches of physics, such as fluid dynamics, electromagnetism and quantum theory. The book will be of use to researchers in signal processing, physics and applied mathematics. Partial differential equations are introduced as an additional tool in signal analysis. The book will be of use to signal processing experts who are interested in developing tools for the analysis of signals arising in real systems.

The mathematical tools used in signal analysis involve differential and difference equations, integral equations, matrix algebra and calculus, complex analysis and probability theory, and random processes. This book applies these tools to problems in various branches of physics like fluid dynamics, electromagnetism, and quantum theory. The book will be of use to research workers in signal processing, as well as to research workers in physics and applied mathematics. Partial differential equations have been introduced here as an additional tool in signal analysis since they are used to describe quantum, electromagnetic, and fluid dynamical phenomena, as well as Einstein's equations of gravitation. The book will be of use to signal processing experts who are interested in developing tools for the analysis of signals arising in real systems.

The book is intended to be a reference for selected problems in engineering, mathematics, and physics covering the fields of Mechanics, Fluid Dynamics, Signal Processing, Electromagnetic field theory, and Quantum Mechanics. Many of the problems introduced in this book appear as a bridge between two seemingly disconnected topics. For example, the section on mechanics contains a section on linear algebra and another section on group representation with reference to image processing. The specialized techniques developed in one field very often find applications in other fields and the collection of problems in this book illustrates this interplay. The book will be of equal use to mathematicians working on applied problems, to physicists interested in applying tools of signal analysis to their research and to signal processing experts who are looking for applications of signal processing methods to physics problems.

With Special Key Features: Over 350 Solved problems An advanced approach to the area of Signals & Systems Features practically oriented problems with solutions A must for every student studying Signals & Systems Problems featured, cater to students from Undergraduate to Research level This book features problems with solutions to all the core areas of Signals and Systems. The ethos of the book is to enable the reader to solve problems that have a practical relevance. This can be the perfect book to follow along with a textbook. Whilst catering to the needs of the undergraduate and graduate students, students with a research bent of mind will also find the book stimulating and challenging enough to formulate their own research problems along the lines suggested by the exercises.