Relativistic Quantum Invariance

Download Relativistic Quantum Invariance full books in PDF, epub, and Kindle. Read online Relativistic Quantum Invariance ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Relativistic Quantum Invariance

Author : Chueng-Ryong Ji
Publisher : Springer Nature
ISBN 13 : 9811979499
Total Pages : 252 pages
Book Rating : 4.8/5 (119 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Invariance by : Chueng-Ryong Ji

Download or read book Relativistic Quantum Invariance written by Chueng-Ryong Ji and published by Springer Nature. This book was released on 2023-12-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the invariant nature of the relativistic quantum field theories utilizing the idea of interpolating the instant form dynamics and the light-front dynamics. While the light-front dynamics (LFD) based on the light-front time was proposed by Dirac in 1949, there has not yet been a salient review on the connection between the LFD and the instant form dynamics (IFD) based on the ordinary time. By reviewing the connection between LFD and IFD using the idea of interpolating the two different forms of the relativistic dynamics, one can learn the distinguished features of each form and how one may utilize those distinguished features in solving the complicated relativistic quantum field theoretic problems more effectively. With the ongoing 12-GeV Jefferson Lab experiments, the internal structures of the nucleon and nuclei are vigorously investigated in particular using the physical observables defined in the LFD rather than in the IFD. This book offers a clear demonstration on why and how the LFD is more advantageous than the IFD for the study of hadron physics, illustrating the differences and similarities between these two distinguished forms of the dynamics. It aims at presenting the basic first-hand knowledge of the relativistic quantum field theories, describing why and how the different forms of dynamics (e.g., IFD and LFD) can emerge in them, connecting the IFD and the LFD using the idea of the interpolation, and demonstrating explicit examples of the interpolation in quantum electrodynamics and other field theories. While the level of presentation is planned mainly for the advanced undergraduate students and the beginning graduate students, the topics of the interpolation between the IFD and the LFD are innovative enough for even the experts in the field to appreciate its usefulness.

An Introduction to Relativistic Quantum Field Theory

Author : Silvan S. Schweber
Publisher : Courier Corporation
ISBN 13 : 0486139603
Total Pages : 930 pages
Book Rating : 4.4/5 (861 download)

DOWNLOAD NOW!

Book Synopsis An Introduction to Relativistic Quantum Field Theory by : Silvan S. Schweber

Download or read book An Introduction to Relativistic Quantum Field Theory written by Silvan S. Schweber and published by Courier Corporation. This book was released on 2013-10-10 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complete, systematic, and self-contained, this text introduces modern quantum field theory. "Combines thorough knowledge with a high degree of didactic ability and a delightful style." — Mathematical Reviews. 1961 edition.

Relativistic Quantum Mechanics

Author : Hartmut Pilkuhn
Publisher : Springer Science & Business Media
ISBN 13 : 366205275X
Total Pages : 244 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics by : Hartmut Pilkuhn

Download or read book Relativistic Quantum Mechanics written by Hartmut Pilkuhn and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics appears as a special case, and classical relativistic mechanics as another one. These special cases are important for giving plausible names to operators, for example "orbital angular momentum", "spin" or "magnetic moment". A subject which is treated for the first time in this book is the theory of binaries in terms of differential equations which have the mathematical structure of the corresponding one-body equations (Klein--Gordon for two spin- less particles, Dirac for two spinor particles).

Relativistic Quantum Mechanics and Quantum Fields

Author : Ta-you Wu
Publisher : World Scientific
ISBN 13 : 9789810206086
Total Pages : 434 pages
Book Rating : 4.2/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics and Quantum Fields by : Ta-you Wu

Download or read book Relativistic Quantum Mechanics and Quantum Fields written by Ta-you Wu and published by World Scientific. This book was released on 1991 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sequel to the well received book, Quantum Mechanics by T Y Wu, this book carries on where the earlier volume ends. This present volume follows the generally pedagogic style of Quantum Mechanics. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as the basic example and ends with an exposition of important issues related to the standard model. The book presents the subject in basic and easy-to-grasp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics.

Lorentz and Poincar Invariance

Author : Jong-Ping Hsu
Publisher : World Scientific
ISBN 13 : 9789812810984
Total Pages : 620 pages
Book Rating : 4.8/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Lorentz and Poincar Invariance by : Jong-Ping Hsu

Download or read book Lorentz and Poincar Invariance written by Jong-Ping Hsu and published by World Scientific. This book was released on 2001 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers provides a broad view of the development of Lorentz and Poincar(r) invariance and spacetime symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincar(r) groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union of the relativity and quantum theories, marking the beginnings of quantum electrodynamics and relativistic quantum mechanics. Ten of the fundamental experiments testing special relativity are also discussed, showing that they actually support a four-dimensional spacetime based on broad Lorentz and Poincar(r) invariance which is more general than and includes the special theory of relativity. The generalization of the concepts of simultaneity, physical time and the nature of the speed of light within a four-dimensional spacetime framework leads to the conclusion that the symmetries embodied by the special theory of relativity can be realized using only a single postulate OCo the principle of relativity for physical laws. Contents: Theoretical Implications of Lorentz and Poincar(r) Invariance: The Dawn of Lorentz and Poincar(r) Invariance (1887OCo1905): Inquiries Regarding the Constancy of the Speed of Light (1908-1910); The Splendid Union of Special Relativity and Quantum Mechanics (1927OCo1949); The Isotropy of the Speed of Light c: A Convenient Assumption (1963OCo1995); The Logically Simplest Theory of Relativity and Its 4-Dimensional Symmetry (1990OCo1994); Experiments for Lorentz and Poincar(r) Invariance: The Fizeau Experiment; The WilsonOCoWilson Experiment; The Observation of the Muon Lifetime Dilation; The MassOCoVelocity Relation Experiment; The Thomas Precession Experiment; and other papers. Readership: Upper-level undergraduates, graduate students, researchers and academics in mathematical physics and theoretical physics."

Relativistic Quantum Mechanics

Author : Lawrence P. Horwitz
Publisher : Springer
ISBN 13 : 9401772614
Total Pages : 214 pages
Book Rating : 4.4/5 (17 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics by : Lawrence P. Horwitz

Download or read book Relativistic Quantum Mechanics written by Lawrence P. Horwitz and published by Springer. This book was released on 2015-08-04 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.

Gauge Theories in Particle Physics

Author : I.J.R. Aitchison
Publisher : CRC Press
ISBN 13 : 9780849387753
Total Pages : 428 pages
Book Rating : 4.3/5 (877 download)

DOWNLOAD NOW!

Book Synopsis Gauge Theories in Particle Physics by : I.J.R. Aitchison

Download or read book Gauge Theories in Particle Physics written by I.J.R. Aitchison and published by CRC Press. This book was released on 2002-09-01 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge Theories in Particle Physics, Volume 1: From Relativistic Quantum Mechanics to QED, Third Edition presents an accessible, practical, and comprehensive introduction to the three gauge theories of the standard model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the electroweak theory. For each of them, the authors provide a thorough discussion of the main conceptual points, a detailed exposition of many practical calculations of physical quantities, and a comparison of these quantitative predictions with experimental results. For this two-volume third edition, much of the book has been rewritten to reflect developments over the last decade, both in the curricula of university courses and in particle physics research. Substantial new material has been introduced that is intended for use in undergraduate physics courses. New introductory chapters provide a precise historical account of the properties of quarks and leptons, and a qualitative overview of the quantum field description of their interactions, at a level appropriate to third year courses. The chapter on relativistic quantum mechanics has been enlarged and is supplemented by additional sections on scattering theory and Green functions, in a form appropriate to fourth year courses. Since precision experiments now test the theories beyond lowest order in perturbation theory, an understanding of the data requires a more sophisticated knowledge of quantum field theory, including ideas of renormalization. The treatment of quantum field theory has therefore been considerably extended so as to provide a uniquely accessible and self-contained introduction to quantum field dynamics, as described by Feynman graphs. The level is suitable for advanced fourth year undergraduates and first year graduates. These developments are all contained in the first volume, which ends with a discussion of higher order corrections in QED; the second volume is devoted to the non-Abelian gauge theories of QCD and the electroweak theory. As in the first two editions, emphasis is placed throughout on developing realistic calculations from a secure physical and conceptual basis.

Relativity, Symmetry, and the Structure of Quantum Theory

Author : William H. Klink
Publisher :
ISBN 13 : 9781681748894
Total Pages : pages
Book Rating : 4.7/5 (488 download)

DOWNLOAD NOW!

Book Synopsis Relativity, Symmetry, and the Structure of Quantum Theory by : William H. Klink

Download or read book Relativity, Symmetry, and the Structure of Quantum Theory written by William H. Klink and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2

Author : William H Klink
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681748916
Total Pages : 108 pages
Book Rating : 4.6/5 (817 download)

DOWNLOAD NOW!

Book Synopsis Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2 by : William H Klink

Download or read book Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2 written by William H Klink and published by Morgan & Claypool Publishers. This book was released on 2018-03-23 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first version of quantum theory, developed in the mid 1920's, is what is called nonrelativistic quantum theory; it is based on a form of relativity which, in a previous volume, was called Newton relativity. But quickly after this first development, it was realized that, in order to account for high energy phenomena such as particle creation, it was necessary to develop a quantum theory based on Einstein relativity. This in turn led to the development of relativistic quantum field theory, which is an intrinsically many-body theory. But this is not the only possibility for a relativistic quantum theory. In this book we take the point of view of a particle theory, based on the irreducible representations of the Poincare group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; we develop what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A central issue in any relativistic quantum theory is how to introduce interactions without spoiling relativistic invariance. We show that interactions can be incorporated in a mass operator, in such a way that relativistic invariance is maintained. Surprisingly for a relativistic theory, such a construction allows for instantaneous interactions; in addition, dynamical particle exchange and particle production can be included in a multichannel formulation of the mass operator. For systems of more than two particles, however, straightforward application of such a construction leads to the undesirable property that clusters of widely separated particles continue to interact with one another, even if the interactions between the individual particles are of short range. A significant part of this volume deals with the solution of this problem. Since relativistic quantum mechanics is not as well-known as relativistic quantum field theory, a chapter is devoted to applications of point form quantum mechanics to nuclear physics; in particular we show how constituent quark models can be used to derive electromagnetic and other properties of hadrons.

Relativistic Quantum Mechanics and Introduction to Field Theory

Author : Francisco J. Yndurain
Publisher : Springer Science & Business Media
ISBN 13 : 3642610579
Total Pages : 342 pages
Book Rating : 4.6/5 (426 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics and Introduction to Field Theory by : Francisco J. Yndurain

Download or read book Relativistic Quantum Mechanics and Introduction to Field Theory written by Francisco J. Yndurain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook supplies graduate students with a primer in quantum theory. A variety of processes are discussed with concepts such as potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory, the author emphasizes the deduction of the said potentials or currents. A modern presentation of the subject together with many exercises, unique in its unusual underlying concept of combining relativistic quantum mechanics with basic quantum field theory.

Relativistic Quantum Mechanics and Quantum Fields

Author : W-Y Pauchy Hwang
Publisher : World Scientific Publishing Company
ISBN 13 : 9813270047
Total Pages : 416 pages
Book Rating : 4.8/5 (132 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics and Quantum Fields by : W-Y Pauchy Hwang

Download or read book Relativistic Quantum Mechanics and Quantum Fields written by W-Y Pauchy Hwang and published by World Scientific Publishing Company. This book was released on 2018-04-26 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Perspectives on Quantum Reality

Author : R.K. Clifton
Publisher : Springer Science & Business Media
ISBN 13 : 940158656X
Total Pages : 246 pages
Book Rating : 4.4/5 (15 download)

DOWNLOAD NOW!

Book Synopsis Perspectives on Quantum Reality by : R.K. Clifton

Download or read book Perspectives on Quantum Reality written by R.K. Clifton and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: But to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics. J. S. Bell, Are There Quantum Jumps? ON CANADIAN THANKSGIVING WEEKEND in the autumn of 1994, a lively conference was held at The University of Western Ontario under the title "Conceptual Problems of Relativistic Quantum Mechanics". Most of the eighteen papers in this volume are directly connected with that conference. Articles by both theoretical physicists and philosophers of science are included, and many authors will be recognized immediately for their already substantive work in the foundations of physics. A quarter century ago Howard Stein suggested that relativistic quantum field theory should be 'the contemporary locus of metaphysical research', but there were few takers. Only fairly recently has that changed, with the result that the bulk of the papers here pursue issues that go beyond nonrelativistic quantum mechanics (or at least have serious implications for its relativistic generalization). Nevertheless, problems interpreting the nonrelativistic theory remain a persistent thorn in the side of any such endeavor, and so some of the papers develop innovative approaches to those issues as well.

Relativistic Quantum Mechanics

Author :
Publisher :
ISBN 13 : 9783662052778
Total Pages : 239 pages
Book Rating : 4.0/5 (527 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Mechanics by :

Download or read book Relativistic Quantum Mechanics written by and published by . This book was released on 2003 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics appear as special cases. They are the sources of familiar names such as "orbital angular momentum", "spin-orbit coupling" and "magnetic moment" for operators of the relativistic quantum formalism. The theory of binaries, in terms of differential equations, is treated for the first time in this book. These have the mathematical structure of the corresponding one-body equations (Klein--Gordon for two spinless particles, Dirac for two spinor particles) with a relativistically reduced mass. They allow the calculation of radiative corrections via the vector potential operator. This second edition of the successful textbook adds various new sections on relativistic quantum chemistry and on the relativistic treatment of the proton in hydrogen. Others chapters have been expanded, e.g. on hyperfinite interactions, or carefully revisited.

Quantum Mechanics with Non-Unitary Symmetries

Author : Bojan Bistrovic
Publisher : Marsonia Press LLC
ISBN 13 : 1734919914
Total Pages : 551 pages
Book Rating : 4.7/5 (349 download)

DOWNLOAD NOW!

Book Synopsis Quantum Mechanics with Non-Unitary Symmetries by : Bojan Bistrovic

Download or read book Quantum Mechanics with Non-Unitary Symmetries written by Bojan Bistrovic and published by Marsonia Press LLC. This book was released on 2020-04-22 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows that with minimal modifications of postulates of non-relativistic quantum mechanics to allow for non-unitary representations of symmetry groups (Lorentz group in particular), one achieves a fully relativistic quantum theory without any of the issues (like negative energies, etc.) that led to the second quantization and QFT. It is shown that quite a few phenomena in elementary particle physics (like for example neutral kaon mixing, CP symmetry and it's supposed breaking) can be explained purely as a consequence of relativistic invariance and relativistic invariance alone. It is shown that by categorizing mesons via the representation of Lorentz group they belong to, one can explain a lot of their properties, as well as a lot of discrepancies in the particle data tables. It is also shown that based on properties of Lorentz representations of products of meson decays, a lot of excited states listed in PDG tables are really several different excitations with similar masses. Relativistic treatment of bound states in momentum space is developed and used to calculate decay widths of various composite particles like Positronium or mesons, and then those decay widths are used to calculate various properties of quarks (like their masses or charges) that were previously misunderstood. In particular, it is shown that quarks are actually quite heavy (around 3.5GeV for up/down quarks) and that while Lorentz invariance allows both fractional values (2/3, -1/3) as well as integer values (2,1), based on (very sparse) available experimental data, integer quark charges are more consistent with observed decay widths than fractional charges.

The Theory of Photons and Electrons

Author : Josef M. Jauch
Publisher : Springer Science & Business Media
ISBN 13 : 3642809510
Total Pages : 569 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!

Book Synopsis The Theory of Photons and Electrons by : Josef M. Jauch

Download or read book The Theory of Photons and Electrons written by Josef M. Jauch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the discovery of the corpuscular nature of radiation by Planck more than fifty years ago the quantum theory of radiation has gone through many stages of development which seemed to alternate between spectacular success and hopeless frustration. The most recent phase started in 1947 with the discovery of the electromagnetic level shifts and the realization that the exist ing theory, when properly interpreted, was perfectly adequate to explain these effects to an apparently unlimited degree of accuracy. This phase has now reached a certain conclusion: for the first time in the checkered history of this field of research it has become possible to give a unified and consistent presen tation of radiation theory in full conformity with the principles of relativity and quantum mechanics. To this task the present book is devoted. The plan for a book of this type was conceived during the year 1951 while the first-named author (J. M. J. ) held a Fulbright research scholarship at Cambridge University. During this year of freedom from teaching and other duties he had the opportunity of conferring with physicists in many different countries on the recent developments in radiation theory. The comments seemed to be almost unanimous that a book on quantum electrodynamics at the present time would be of inestimable value to physicists in many parts of the world. However, it was not until the spring of 1952 that work on the book began in earnest.

Gauge Theories in Particle Physics: A Practical Introduction

Author : Ian J R Aitchison
Publisher : CRC Press
ISBN 13 : 1466512997
Total Pages : 456 pages
Book Rating : 4.4/5 (665 download)

DOWNLOAD NOW!

Book Synopsis Gauge Theories in Particle Physics: A Practical Introduction by : Ian J R Aitchison

Download or read book Gauge Theories in Particle Physics: A Practical Introduction written by Ian J R Aitchison and published by CRC Press. This book was released on 2012-12-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED). The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a unique elementary introduction to quantum field theory, establishing the essentials of the formal and conceptual framework upon which the subsequent development of the three gauge theories is based. The text also describes tree-level calculations of physical processes in QED and introduces ideas of renormalization in the context of one-loop radiative corrections for QED. New to the Fourth Edition New chapter on Lorentz transformations and discrete symmetries in relativistic quantum mechanics, with physical applications Introduction of Majorana fermions at an early stage, making the material suitable for a first course in relativistic quantum mechanics Discrete symmetries in quantum field theory Updates on nucleon structure functions and the status of QED The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight.

Relativistic Quantum Dynamics

Author : Eugene Stefanovich
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110493225
Total Pages : 241 pages
Book Rating : 4.1/5 (14 download)

DOWNLOAD NOW!

Book Synopsis Relativistic Quantum Dynamics by : Eugene Stefanovich

Download or read book Relativistic Quantum Dynamics written by Eugene Stefanovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of three, quantum electrodynamics is formulated in the language of physical „dressed" particles. A theory where charged particles interact via instantaneous action-at-a-distance forces is constructed - without need for renormalization. This theory describes electromagnetic phenomena in terms of directly interacting charges, but in full accord with fundamental principles of relativity and causality. Contents Three ways to look at QFT Dressing What are advantages of dressed Hamiltonian? Coulomb potential and beyond Decays RQD in higher orders Classical electrodynamics Experimental support of RQD Particles and relativity Special theory of relativity Unitary dressing transformation Integral for decay law Coulomb scattering integral in fourth order Relativistic invariance of Coulomb–Darwin–Breit electrodynamics