Developments in Mathematical and Conceptual Physics (eBook)

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).

Dr. Harish Parthasarathy completed his B.Tech. in Electrical Engineering from IIT Kanpur in 1990 and Ph.D. from IIT Delhi in 1994 in Signal Processing. His doctoral work was on developing high-resolution bispectrum estimation algorithms which find application in EEG data analysis. His postdoctoral work was on developing algorithms for galactic simulation and the study of gravitating systems in the presence of noise. He is currently Professor at Netaji Subhas University of Technology where he has taught courses on signals, electromagnetics and statistical signal processing. His research interests include applications of group representation theory to image processing, recovery of MRI from EEG data via statistical signal processing algorithms, quantum gate design using field theory and quantum gravity, supersymmetry and superstring theory. He has also guided many projects on applications of large deviation theory to the robot stability problem. He is the author of over 20 books and 130 research papers in national and international journals and conferences.

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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).