# High-Field Electrodynamics

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## Book Description

Tremendous technological developments and rapid progress in theory have opened a new area of modern physics called high-field electrodynamics: the systematic study of the interaction of relativistic electrons or positrons with ultrahigh-intensity, coherent electromagnetic radiation.

This advanced undergraduate/graduate-level text provides a detailed introduction to high-field electrodynamics, from its fundamentals to some of its important modern applications. The author describes a broad collection of theoretical techniques, and where possible, approaches derivations by at least two different routes to yield deeper physical insight and a wider range of mathematical and physical techniques. He also discusses some of the outstanding ramifications of electrodynamics in areas ranging from quantum optics, squeezed states, and the Einstein-Podolsky-Rosen paradox to rotating black holes, non-Abelian gauge field theories, and the Bohm-Aharanov effect.

High-Field Electrodynamics gives a comprehensive description of the theoretical tools needed to approach this novel discipline. It highlights important modern applications and serves as a starting point for more advanced and specialized research at the frontiers of modern physics.

## Table of Contents

FOUNDATIONS

Overview

The Relativistic Intensity Regime

The Schwinger Critical Field

Maxwell's Equations

Fields & Inductions, the Minkowski Formalism

Potentials, Gauge Condition, & Wave Equation

The Coulomb Potential & Plane Waves

The Lorentz Transformation

The Special Lorentz Transform

Four-Vectors

Addition of Velocities

Four-Acceleration & Hyperbolic Motion

Variation of the Mass with Velocity

The Energy-Momentum 4-Vector

Transformation of Forces

Transformation of Energy

Transformation of Angular Momentum

Transformation of Length, Surface, Volume & Density

Relativistic Plasma Frequency

The General Lorentz Transform

Thomas Precession

Schwinger's Approach

References

Covariant Electrodynamics

Four-Vectors & Tensors

The Electromagnetic Field Tensor

Covariant Form of the Maxwell-Lorentz Equations

A Few Invariants, 4-Vectors, & Tensors Commonly Used

Transformation of the Fields

Electron & QED Units

Covariant Electromagnetic Lagrangian & Hamiltonian

Field 4-Momentum & Maxwell Stress Tensor

Metric & Christoffel Symbols

Solid in Rotation, Sagnac Effect

Dual Tensors & Spinors, Dirac Equation

Notes

References

Gauge Condition & Transform

Lorentz Gauge

Coulomb Gauge & Instantaneous Scalar Potential

Other Gauge Conditions

Charge Conservation

Noether's Theorem

Yang-Mills and Non-Abelian Gauge Fields

Weyl's Theory

Kaluza-Klein 5-Dimensional Space-Time

Charged Black Holes, Quantum Gravity, & Inflation

Superstrings and Dimensionality

The Bohm-Aharanov Effect

ELECTROMAGNETIC WAVES

Green & Delta Functions, Eigenmode Theory of Waveguides

Introduction

The Dirac Delta Function

Fourier, Laplace, & Hankel Transforms

Green Functions in Vacuum

Liénard-Wiechert Potentials

Green Functions with Boundary Conditions: Cylindrical Waveguide

Point Charge in Rectilinear Motion in Vacuum

Multipoles, Spherical Harmonics & the H Atom

Group Velocity Dispersion, Higher-Order Effects, and Solitons

Plane Waves & Photons

Quantization of the Free Electromagnetic Field

Creation & Annihilation Operators

Energy and Number Spectra

Momentum of the Quantized Field

Angular Momentum of the Quantized Field

Classical Spin of the Electromagnetic Field

Photon Spin

Vacuum Fluctuations

The Einstein-Podolsky-Rosen Paradox

Squeezed States

Casimir Effect

Reflection of Plane Waves in Rindler Space

Relativistic Transform of the Refractive Index: Cerenkov Radiation

Classical Theory of Cerenkov Radiation

Fields and Inductions, Polarization and Nonlinear Susceptibilities

Transform of Linear Refractive Index: Minkowski Formulation

Anomalous Refractive Index & Cerenkov Effect

Linear Isotropic Medium: Induced-Source Formalism

Covariant treatment of Nonlinear Effects

Three-Dimensional Waves in Vacuum, Ponderomotive Scattering, Vacuum Laser Acceleration

Exact Solutions to the 3D Wave Equation in Vacuum

The Paraxial Propagator

Bessel Functions & Hankel's Integral Theorem

Plane Wave Dynamics, Lawson-Woodward Theorem

Ponderomotive Scattering

Electron Dynamics in a Coherent Dipole Field

Chirped-pulse Inverse Free-Electron Laser

Free-Wave Acceleration by Stimulated Absorption of Radiation

Plasma-Based Laser Acceleration Processes

RELATIVISTIC ELECTRONS AND RADIATION

Coherent Synchrotron Radiation, Relativistic Fluid Theory

Coherent Synchrotron Radiation in Free-Space

Coherent Synchrotron Radiation in a Waveguide

Instantaneous Power Flow in the Waveguide

Time-Dependent Chirped Wavepacket

Propagation in Negative GVD Structure

Relativistic Eulerian Fluid Perturbation Theory

Compton Scattering, Coherence, and Radiation Reaction

Classical Theory of Compton Scattering

Electron Beam Phase Space

Three-Dimensional Theory of Compton Scattering

Stochastic Electron Gas Theory of Coherence

Harmonics and Nonlinear Radiation Pressure

Radiative Corrections: Overview

Symmetrized Electrodynamics: Introduction

Symmetrized Electrodynamics: Complex Notation

Symmetrized Direct-Lorentz Equation

Conceptual Difficulties: Electromagnetic Mass Renormalization, Runaways, Acausal Effects

Schott Term

Maxwell Stress Tensor

Hamiltonian Formalism

Symmetrized Electrodynamics in the Complex Charge Plane and the Running Fine Structure Constant

Bibliography

References

Index

Each chapter also contains Notes and References sections

## Reviews

"This book is a complete guide to the understanding of how current photonics instrumentation works...Undoubtedly useful for biomedical engineers and physicians who need to have an essential reference that encompasses all areas of photonics."

- Valentin Grimblatov, Ph.D., Columbia-Presbyterian Medical Center, in IEEE Engineering in Medicine and Biology, 1997