**Author**: Reinhard Honegger

**Publisher:**World Scientific Publishing Company Incorporated

**ISBN:**9789814618823

**Category :**Science

**Languages :**en

**Pages :**2250

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## Photons in Fock Space and Beyond

**Author**: Reinhard Honegger

**Publisher:** World Scientific Publishing Company Incorporated

**ISBN:** 9789814618823

**Category : **Science

**Languages : **en

**Pages : **2250

**Book Description**

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.

## Photons in Fock Space and Beyond

**Author**: Reinhard Honegger

**Publisher:** World Scientific Publishing Company Incorporated

**ISBN:** 9789814618823

**Category : **Science

**Languages : **en

**Pages : **2250

**Book Description**

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.

## Photons in Fock Space and Beyond

**Author**: Reinhard Honegger

**Publisher:** World Scientific

**ISBN:** 9814618853

**Category : **Science

**Languages : **en

**Pages : **656

**Book Description**

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise. A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems. Contents:Volume I: From Classical to Quantized Radiation Systems:Preliminaries on ElectromagnetismClassical Electrodynamics in L2-Hilbert SpacesClassical Electrodynamics in the Smeared Field FormalismStatistical Classical ElectrodynamicsCanonical Quantization and Weyl AlgebrasDeformation QuantizationOptical States, Optical CoherenceVolume II: Quantized Mesoscopic Radiation Models:SqueezingBlack Body RadiationMesoscopic Electronic Matter Algebras and StatesWeakly Inhomogeneous InteractionsQuantized Radiation ModelsVolume III: Mathematics for Photon Fields:Observables and AlgebrasStates and Their Decomposition MeasuresDynamics and Perturbation TheoryGauges and Fiber Bundles Readership: This three-volume series is recommended for graduate students and researchers working in rigorous Electrodynamics, Quantum Optics and Quantum Field Theory in general. Key Features:On the side of Physics, “Photons in Fock Space and Beyond” extends the applicability of quantum optical notions far beyond the usual scope of the quantum optical literature by using more general optical cavities and theoretical ansatzes. By establishing a systematic conceptual frame, many fundamental questions of photon theory are clarified by mathematical argumentsOn the side of Mathematical Physics, certain parts of the theory of vector fields with boundary conditions, of operator algebras, ergodic theory, convexity, measures on dual spaces, perturbation theory and electrodynamic gauge bundles are not only treated in an introductory fashion but also supplemented in an original mannerThe unique feature of that exposition of mathematical disciplines is their integration into a comprehesive line of thought within a deductive physical theoryKeywords:Electrodynamics;Vector Analysis;Statistical Physics;Quantum Optics;Quantum Field Theory;Quantum Statistics;Solid State Physics;Superconductivity;Gauge Theory;Operator Algebras;Convexity;Topological Vector Spaces;Fiber BundlesReviews: “This three volume work on the quantum field theory of radiation combines well presented, competent mathematical foundations with actual physical applications to mesoscopic photonics.” (See Full Review) Professor Ernst Binz Universität Mannheim

## The Quantization of Gravity

**Author**: Claus Gerhardt

**Publisher:** Springer

**ISBN:** 3319773712

**Category : **Science

**Languages : **en

**Pages : **200

**Book Description**

A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.

## The Geometry of Heisenberg Groups

**Author**: Ernst Binz

**Publisher:** American Mathematical Soc.

**ISBN:** 0821844954

**Category : **Mathematics

**Languages : **en

**Pages : **299

**Book Description**

This book presents basic geometric and algebraic properties of the Heisenberg group and its relation to the skew field of quaternions, symplectic structures and representations, and describes some of its applications. It offers a clear exposition of mathematical topics referring to applications in signal theory, physics and information theory. It has relevance for undergraduate and graduate students, a variety of researchers, and specialists in data processing.

## Fundamental Physics — Heisenberg and Beyond

**Author**: Gerd W. Buschhorn

**Publisher:** Springer Science & Business Media

**ISBN:** 3642186238

**Category : **Science

**Languages : **en

**Pages : **189

**Book Description**

Presents two essays commemorating Werner Heisenberg's 100th birthday, which are complemented by a short and nicely illustrated biographical note in the appendix. In the second part, the reader will find a spectrum of articles devoted to important developments in central areas of research by authors are outstanding scientists. Contributions on modern developments by eminent physicists such as Anton Zeilinger, Julius Weiss, Elliott Lieb, Michael Peskin, Jürg Frölich, Alan Watson, and others.

## Phase Space Picture of Quantum Mechanics

**Author**: Y. S. Kim

**Publisher:** World Scientific

**ISBN:** 9789810203610

**Category : **Science

**Languages : **en

**Pages : **356

**Book Description**

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrdinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

## Mathematics Unlimited - 2001 and Beyond

**Author**: Björn Engquist

**Publisher:** Springer

**ISBN:** 364256478X

**Category : **Mathematics

**Languages : **en

**Pages : **1236

**Book Description**

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

## Theory of Nonclassical States of Light

**Author**: V.V. Dodonov

**Publisher:** CRC Press

**ISBN:** 1482288222

**Category : **Technology & Engineering

**Languages : **en

**Pages : **384

**Book Description**

The term 'nonclassical states' refers to the quantum states that cannot be produced in the usual sources of light, such as lasers or lamps, rather than those requiring more sophisticated apparatus for their production. Theory of Non-classical States of Light describes the current status of the theory of nonclassical states of light including many new and important results as well as introductory material and the history of the subject. The authors concentrate on the most important types of nonclassical states, namely squeezed, even/odd ('Schrodinger cat') and binomial states, including their generalizations. However, a review of other types of nonclassical is also given in the introduction, and methods for generating nonclassical states on various processes of light-matter interaction, their phase-space description, and the time evolution of nonclassical states in these processes is presented in separate chapters. This contributed volume contains all of the necessary formulae and references required to gain a good understanding of the principles and current status of the field. It will provide a valuable information resource for advanced students and researchers in quantum physics.

## Theory and Practice of Natural Computing

**Author**: Carlos Martín-Vide

**Publisher:** Springer Nature

**ISBN:** 3030630005

**Category : **Computers

**Languages : **en

**Pages : **171

**Book Description**

This book constitutes the refereed proceedings of the 9th International Conference on Theory and Practice of Natural Computing, TPNC 2020, held in Taoyuan, Taiwan, in December 2020. The 12 full papers presented in this book, together with one invited talk, were carefully reviewed and selected from 24 submissions. The papers are organized in topical sections named: applications of natural computing; quantum computing and unconventional computing; and swarm intelligence, evolutionary algorithms, and DNA computing.

## Relativistic Many-Body Theory

**Author**: Ingvar Lindgren

**Publisher:** Springer

**ISBN:** 3319153862

**Category : **Science

**Languages : **en

**Pages : **406

**Book Description**

This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into three parts. In Part I, the standard time-independent and time-dependent perturbation procedures are reviewed. This includes a new section at the end of chapter 2 concerning the so-called ”Fock-space procedure” or ”Coulomb-only procedure” for relativistic-QED calculations . This is a procedure on an intermediate level, frequently used in recent time by chemists on molecular systems, where a full QED treatment is out of question. Part II describes three methods for QED calculations, a) the standard S-matrix formulation, b) the Two-times Green’s-function method, developed by the St Petersburg Atomic Theory group, and c) the Covariant-evolution operator (CEO) method, recently developed by the Gothenburg Atomic Theory group. In Part III, the CEO method is combined with electron correlation to arbitrary order to a unified MBPT-QED procedure. The new Part IV includes two new chapters dealing with dynamical properties and how QED effects can be evaluated for such processes. This part is much needed as there has been an increasing interest in the study of QED effects for such processes. All methods treated in the book are illustrated with numerical examples, making it a text suitable for advanced students new to the field and a useful reference for established researchers.

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The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise. A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems. Contents:Volume I: From Classical to Quantized Radiation Systems:Preliminaries on ElectromagnetismClassical Electrodynamics in L2-Hilbert SpacesClassical Electrodynamics in the Smeared Field FormalismStatistical Classical ElectrodynamicsCanonical Quantization and Weyl AlgebrasDeformation QuantizationOptical States, Optical CoherenceVolume II: Quantized Mesoscopic Radiation Models:SqueezingBlack Body RadiationMesoscopic Electronic Matter Algebras and StatesWeakly Inhomogeneous InteractionsQuantized Radiation ModelsVolume III: Mathematics for Photon Fields:Observables and AlgebrasStates and Their Decomposition MeasuresDynamics and Perturbation TheoryGauges and Fiber Bundles Readership: This three-volume series is recommended for graduate students and researchers working in rigorous Electrodynamics, Quantum Optics and Quantum Field Theory in general. Key Features:On the side of Physics, “Photons in Fock Space and Beyond” extends the applicability of quantum optical notions far beyond the usual scope of the quantum optical literature by using more general optical cavities and theoretical ansatzes. By establishing a systematic conceptual frame, many fundamental questions of photon theory are clarified by mathematical argumentsOn the side of Mathematical Physics, certain parts of the theory of vector fields with boundary conditions, of operator algebras, ergodic theory, convexity, measures on dual spaces, perturbation theory and electrodynamic gauge bundles are not only treated in an introductory fashion but also supplemented in an original mannerThe unique feature of that exposition of mathematical disciplines is their integration into a comprehesive line of thought within a deductive physical theoryKeywords:Electrodynamics;Vector Analysis;Statistical Physics;Quantum Optics;Quantum Field Theory;Quantum Statistics;Solid State Physics;Superconductivity;Gauge Theory;Operator Algebras;Convexity;Topological Vector Spaces;Fiber BundlesReviews: “This three volume work on the quantum field theory of radiation combines well presented, competent mathematical foundations with actual physical applications to mesoscopic photonics.” (See Full Review) Professor Ernst Binz Universität Mannheim

A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.

This book presents basic geometric and algebraic properties of the Heisenberg group and its relation to the skew field of quaternions, symplectic structures and representations, and describes some of its applications. It offers a clear exposition of mathematical topics referring to applications in signal theory, physics and information theory. It has relevance for undergraduate and graduate students, a variety of researchers, and specialists in data processing.

Presents two essays commemorating Werner Heisenberg's 100th birthday, which are complemented by a short and nicely illustrated biographical note in the appendix. In the second part, the reader will find a spectrum of articles devoted to important developments in central areas of research by authors are outstanding scientists. Contributions on modern developments by eminent physicists such as Anton Zeilinger, Julius Weiss, Elliott Lieb, Michael Peskin, Jürg Frölich, Alan Watson, and others.

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrdinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

The term 'nonclassical states' refers to the quantum states that cannot be produced in the usual sources of light, such as lasers or lamps, rather than those requiring more sophisticated apparatus for their production. Theory of Non-classical States of Light describes the current status of the theory of nonclassical states of light including many new and important results as well as introductory material and the history of the subject. The authors concentrate on the most important types of nonclassical states, namely squeezed, even/odd ('Schrodinger cat') and binomial states, including their generalizations. However, a review of other types of nonclassical is also given in the introduction, and methods for generating nonclassical states on various processes of light-matter interaction, their phase-space description, and the time evolution of nonclassical states in these processes is presented in separate chapters. This contributed volume contains all of the necessary formulae and references required to gain a good understanding of the principles and current status of the field. It will provide a valuable information resource for advanced students and researchers in quantum physics.

This book constitutes the refereed proceedings of the 9th International Conference on Theory and Practice of Natural Computing, TPNC 2020, held in Taoyuan, Taiwan, in December 2020. The 12 full papers presented in this book, together with one invited talk, were carefully reviewed and selected from 24 submissions. The papers are organized in topical sections named: applications of natural computing; quantum computing and unconventional computing; and swarm intelligence, evolutionary algorithms, and DNA computing.

This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into three parts. In Part I, the standard time-independent and time-dependent perturbation procedures are reviewed. This includes a new section at the end of chapter 2 concerning the so-called ”Fock-space procedure” or ”Coulomb-only procedure” for relativistic-QED calculations . This is a procedure on an intermediate level, frequently used in recent time by chemists on molecular systems, where a full QED treatment is out of question. Part II describes three methods for QED calculations, a) the standard S-matrix formulation, b) the Two-times Green’s-function method, developed by the St Petersburg Atomic Theory group, and c) the Covariant-evolution operator (CEO) method, recently developed by the Gothenburg Atomic Theory group. In Part III, the CEO method is combined with electron correlation to arbitrary order to a unified MBPT-QED procedure. The new Part IV includes two new chapters dealing with dynamical properties and how QED effects can be evaluated for such processes. This part is much needed as there has been an increasing interest in the study of QED effects for such processes. All methods treated in the book are illustrated with numerical examples, making it a text suitable for advanced students new to the field and a useful reference for established researchers.