Quantum Antennas

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Chapter 1: Basic quantum electrodynamics required for the analysis of quantum antennas
	1.1 Introduction
	1.2 The problems to be discussed
	1.3 EM field Lagrangian density
	1.4 Electric and magnetic fields in special relativity
	1.5 Canonical position and momentum fields in electrodynamics
	1.6 The matter fields in electrodynamics
	1.7 The Dirac bracket in electrodynamics
	1.8 Hamiltonian of the em field
	1.9 Interaction Hamiltonian between the current field and the electromagnetic field
	1.10 The Boson commutation relations for the creation and annihilation operator fields for the EM field in momentum-spin domain
	1.11 Electrodynamics in the Coulomb gauge
	1.12 The Dirac second quantized field
	1.13 The Dirac equation in an EM field, approximate solution using Perturbation theory
	1.14 Electromagnetically perturbed Dirac current
Chapter 2: Effects of the gravitational field on a quantum antenna and some basic non-Abelian gauge theory
	2.1 The effect of a gravitational field on photon paths
	2.2 Interaction of gravitation with the photon field
	2.3 Quantum description of the effect of the gravitational field on the photon propagator
	2.4 Electrons and positrons in a mixture of the gravitational field and an EM field Quantum antennas in a background gravitational field
	2.5 Dirac equation in a gravitational field and a quantum white noise photon field described in the Hudson-Parthasarathy formalism
	2.6 Dirac-Yang-Mills current density for non-Abelian gauge theories
	2.7 Dirac brackets
	2.8 Harish-Chandra’s discrete series representations of SL(2,R) and its application to pattern recognition under Lorentz transformations in the plane
	2.9 Estimating the shape of the antenna surface from the scattered EM field when an incident EM field induces a surface current density on the antenna that is determined by Pocklington’s integral equation obtained by setting the tangential component of the total incident plus scattered electric field on the surface to zero
	2.10 Surface current density operator induced on the surface of a quantum antenna when a quantum EM field is incident on it
	2.11 Summary of the second quantized Dirac field
	2.12 Electron propagator computation
	2.13 Quantum mechanical tunneling of a Dirac particle through the critical radius of the Schwarzchild blackhole
	2.14 Supersymmetry-supersymmetric current in an antenna comprising superpartners of elementary particles
Chapter 3: Conducting fluids as quantum antennas
	3.1 A short course in basic non-relativistic and relativistic fluid dynamics with antenna theory applications
	3.2 Flow of a 2-D conducting fluid
	3.3 Finite element method for solving the fluid dynamical equations
	3.4 Elimination of pressure, incompressible fluid dynamics in terms of just a single stream function vector field with vanishing divergence
	3.5 Fluids driven by random external force fields
	3.6 Relativistic fluids, tensor equations
	3.7 General relativistic fluids, special solutions
	3.8 Galactic evolution using perturbed fluid dynamics, dispersive relations. The unperturbed metric is the Roberson-Walker metric corresponding to a homogeneous and isotropic universe
	3.9 Magnetohydrodynamics-diffusion of the magnetic field and vorticity
	3.10 Galactic equation using perturbed Newtonian fluids
	3.11 Plotting the trajectories of fluid particles
	3.12 Statistical theory of fluid turbulence, equations for the velocity field moments, the Kolmogorov-Obhukov spectrum
	3.13 Estimating the velocity field of a fluid subject to random forcing using discrete space velocity measurements based on discretization and the Extended Kalman filter
	3.14 Quantum fluid dynamics. Quantization of the fluid velocity field by the introduction of an auxiliary Lagrange multiplier field
	3.15 Optimal control problems for fluid dynamics
	3.16 Hydrodynamic scaling limits for simple exclusion models
	3.17 Appendix: The complete fluid dynamical equations in orthogonal curvilinear coordinate systems specializing to cylindrical and spherical polar coordinates
Chapter 4: Quantum robots in motion carrying Dirac current as quantum antennas
	4.1 A short course in classical and quantum robotics with antenna theory applications
	4.2 A fluid of interacting robots
	4.3 Disturbance observer in a robot
	4.4 Robot connected to a spring mass with damping system
Chapter 5: Design of quantum gates using electrons, positrons and photons, quantum information theory and quantum stochastic filtering
	5.1 A short course in quantum gates, quantum computation and quantum information with antenna theory applications
	5.2 The Baker-Campbell-Hausdor formula. A, B are n x n matrices
	5.3 Yang-Mills radiation field (an approximation)
	5.4 Belavkin filter applied to estimating the spin of an electron in an external magnetic field. We assume that the magnetic field is B0(t) ∈ R3
Chapter 6: Pattern classification for image fields in motion using Lorentz group representations
	6.1 SL(2,C), SL(2,R) and image processing
Chapter 7: Optimization problems in classical and quantum stochastics and information with antenna design applications
	7.1 A course in optimization techniques
	7.2 Group theoretical techniques in optimization theory
	7.3 Feynman's diagrammatic approach to computation of the scattering amplitudes of electrons, positrons and photons
Chapter 8: Quantum waveguides and cavity resonators
	8.1 Quantum waveguides
Chapter 9: Classical and quantum filtering and control based on Hudson-Parthasarathy calculus, and filter design methods
	9.1 Belavkin filter and Luc-Bouten control for electron spin estimation and quantum Fourier transformed state estimation when corrupted by quantum noise
	9.2 General Quantum filtering and control
	9.3 Some topics in quantum filtering theory
	9.4 Filter design for physical applications
Chapter 10: Gravity interacting with waveguide quantum fields with filtering and control
	10.1 Waveguides placed in the vicinity of a strong gravitational field
	10.2 Some study projects regarding waveguides and cavity resonators in a gravitational field
	10.3 A comparison between the EKF and Wavelet based block processing algorithms for estimating transistor parameters in an amplifier drived by the Ornstein-Uhlenbeck process
	10.4 Computing the Haar measure on a Lie group using left invariant vector fields and left invariant one forms
	10.5 How background em radiation affects the expansion of the universe
	10.6 Stochastic BHJ equations in discrete and continuous time for stochastic optimal control based on instantaneous feedback
	10.7 Quantum stochastic optimal control of the HP-Schrodinger equation
	10.8 Bath in a superposition of coherent states interacting with a system
Chapter 11: Basic triangle geometry required for understanding Riemannian geometry in Einstein’s theory of gravity
	11.1 Problems in mathematics and physics for school students
	11.2 Geometry on a curved surface, study problems
Chapter 12: Design of gates using Abelian and non-Abelian gauge quantum field theories with performance analysis using the Hudson-Parthasarathy quantum stochastic calculus
	12.1 Design of quantum gates using Feynman diagrams
	12.2 An optimization problem in electromagnetism
	12.3 Design of quantum gates using non-Abelian gauge theories
	12.4 Design of quantum gates using the Hudson-Parthasarathy quantum stochastic Schrodinger equation
	12.5 Gravitational waves in a background curved metric
	12.6 Topics for a short course on electromagnetic field propagation at high frequencies
Chapter 13: Quantum gravity with photon interactions, cavity resonators with inhomogeneities, classical and quantum optimal control of fields
	13.1 Quantum control of the HP-Schrodinger equation by state feedback
	13.2 Some ppplications of poisson processes
	13.3 A problem in optimal control
	13.4 Interaction between photons and gravitons
	13.5 A version of quantum optimal control
	13.6 A neater formulation of the quantum optimal control problem
	13.7 Calculating the approximate shift in the oscillation frequency of a cavity resonator having arbitrary cross section when the medium has a small inhomogeneity
	13.8 Optimal control for partial dierential equations
Chapter 14: Quantization of cavity fields with inhomogeneous media, field dependent media parameters from Boltzmann-Vlasov equations for a plasma, quantum Boltzmann equation for quantum radiation pattern computation, optimal control of classical fields, applications classical nonlinear filtering
	14.1 Computing the shift in the characteristic frequencies of oscillation in a cavity resonator due to gravitational effects and the effect of non-uniformity in the medium
	14.2 Quantization of the field in a cavity resonator having non-uniform permittivity and permeability
	14.3 Problems in transmission lines and waveguides
	14.4 Problems in optimization theory
	14.5 Another approach to quantization of wave-modes in a cavity resonator having non-uniform medium based on the scalar wave equation
	14.6 Derivation of the general structure of the field dependent permittivity and permeability of a plasma
	14.7 Other approaches to calculating the permittivity and permeability of a plasma via the use of Boltzmann's kinetic transport equation
	14.8 Derivation of the permittivity and permeability functions using quantum statistics
	14.9 Approximate discrete time nonlinear filtering for non-Gaussian process and measurement noise
	14.10 Quantum theory of many body systems with application to current computation in a Fermi liquid
	14.11 Optimal control of gravitational, matter and em fields
	14.12 Calculating the modes in a cylindrical cavity resonator with a partition in the middle
	14.13 Summary of the algorithm for nonlinear filtering in discrete time applied to fan rotation angle estimation
	14.14 Classical filtering theory applied to Levy process and Gaussian measurement noise. Developing the EKF for such problems
	14.15 Quantum Boltzmann equation for calculating the radiation fields produced by a plasma
Chapter 15: Classical and quantum drone design
	15.1 Project proposal on drone design for the removal of pests in a farm
	15.2 Quantum drones based on Dirac's relativistic wave equation
Chapter 16: Current in a quantum antenna
	16.1 Hartree-Fock equations for obtaining the approximate current density produced by a system of interacting electrons
	16.2 Controlling the current produced by a single quantum charged particle quantum antenna
Chapter 17: Photons in a gravitational field with gate design applications and image processing in electromagnetics
	17.1 Some remarks on quantum blackhole physics
	17.2 EM field pattern produced by a rotated and translated antenna with noise deblurring
	17.3 Estimation of the 3-D rotation and translation vector of an antenna from electromagnetic field measurements
	17.4 Mackey’s theory of induced representations applied to estimating the Poincare group element from image pairs
	17.5 Effect of electromagnetic radiation on the expanding universe
	17.6 Photons inside a cavity
	17.7 Justication of the Hartree-Fock Hamiltonian using second order quantum mechanical perturbation theory
	17.8 Tetrad formulation of the Einstein-Maxwell field equations
	17.9 Optimal quantum gate design in the presence of an electromagnetic field propagating in the Kerr metric
	17.10 Maxwell’s equations in the Kerr metric in the tetrad formalism
Chapter 18: Quantum fluid antennas interacting with media
	18.1 Quantum MHD antenna in a quantum gravitational field
	18.2 Applications of scattering theory to quantum antennas
	18.3 Wave function of a quantum field with applications to writing down the Schrodinger equation for the expanding universe
	18.4 Simple exclusion process and antenna theory
	18.5 MHD and quantum antenna theory
	18.6 Approximate Hamiltonian formulation of the diffusion equation with applications to quantum antenna theory
	18.7 Derivation of the damped wave equation for the electromagnetic field in a conducting media in quantum mechanics using the Lindblad formalism
	18.8 Boson-Fermion unication in quantum stochastic calculus
References