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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 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.
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).
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 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 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.
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 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 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 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 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 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 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 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.
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