# krainaksiazek relativistic quantum theory of particles ii 20124304

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### Relativistic Many-Body Theory Springer, Berlin

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This revised edition of the author s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory. 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 Relativistic Many-Body Theory are illustrated with numerical examples.§

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### Relativistic Quantum Physics Cambridge University Press

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Quantum physics and special relativity theory were two of the greatest breakthroughs in physics during the twentieth century and contributed to paradigm shifts in physics. This book combines these two discoveries to provide a complete description of the fundamentals of relativistic quantum physics, guiding the reader effortlessly from relativistic quantum mechanics to basic quantum field theory. The book gives a thorough and detailed treatment of the subject, beginning with the classification of particles, the Klein

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### Relativistic Quantum Mechanics. Wave Equations Springer, Berlin

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Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.

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### Physical Principles of the Quantum Theory Dover Childrens Books

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I. INTRODUCTORY 1. Theory and Experiment 2. The Fundamental Concepts of Quantum Theory a) Wilson Photographs b) "Diffraction of Matter Waves (Davisson and Germer, Thomson, Rupp)" c) The Diffraction of X-Rays d) The Compton-Simon Experiment e) The Collision Experiments of Franck and Hertz II. CRITIQUE OF THE PHYSICAL CONCEPTS OF THE CORPUSCULAR THEORY 1. The Uncertainty Relations 2. Illustrations of the Uncertainty Relations a) Determination of the Position of a Free Particle b) Measurement of the Velocity or Momentum of a Free Particle c) Bound Electrons d) Energy Measurements III. CRITIQUE OF THE PHYSICAL CONCEPTS OF THE WAVE THEORY 1. The Uncertainty Relations for Waves 2. Discussion of an Actual Measurement of the Electromagnetic Field IV. THE STATISTICAL INTERPRETATION OF QUANTUM THEORY 1. Mathematical Considerations 2. Interference of Probabilities 3. Bohr's Concept of Complementarity V. DISCUSSION OF IMPORTANT EXPERIMENTS 1. The C. T. R. Wilson Experiments 2. Diffraction Experiments 3. The Experiment of Einstein and Rupp 4. "Emission, Absorption, and Dispersion of Radiation" a) Application of the Conservation Laws b) Correspondence Principle and the Method of Virtual Charges c) The Complete Treatment of Radiation and Matter 5. Interference and the Conservation Laws 6. The Compton Effect and the Compton-Simon Experiment 7. Radiation Fluctuation Phenomena 8. Relativistic Formulation of the Quantum Theory APPENDIX: THE MATHEMATICAL APPARATUS OF THE QUANTUM THEORY 1. The Corpuscular Concept of Matter 2. The Transformation Theory 3. The Schršdinger Equation 4. The Perturbation Method 5. Resonance between Two Atoms: the Physical Interpretation of the Transformation Matrices 6. The Corpuscular Concept for Radiation 7. Quantum Statistics 8. The Wave Concept for Matter and Radiation: Classical Theory 9. Quantum Theory of Wave Fields 10. Application to Waves of Negative Charge 11. Proof of the Mathematical Equivalence of the Quantum Theory of Particles and of Waves 12. Application to the Theory of Radiation INDEX

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### An Introduction to Relativistic Processes and the Standard Model of Electroweak Interactions, 1 Springer, Berlin

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This book offers a self-contained introduction to the theory of electroweak interactions based on the semi-classical approach to relativistic quantum field theory, with thorough discussion of key aspects of the field. The basic tools for the calculation of cross sections and decay rates in the context of relativistic quantum field theory are reviewed in a short, but complete and rigorous, presentation. Special attention is focused on relativistic scattering theory and on calculation of amplitude in the semi-classical approximation. The central part of the book is devoted to an illustration of the unified field theory of electromagnetic and weak interactions as a quantum field theory with spontaneously broken gauge invariance; particular emphasis is placed on experimental confirmations of the theory. The closing chapters address the most recent developments in electroweak phenomenology and provide an introduction to the theory and phenomenology of neutrino oscillations. In this 2nd edition the discussion of relativistic scattering processes in the semi-classical approximation has been revised and as a result intermediate results are now explicitly proven. Furthermore, the recent discovery of the Higgs boson is now taken into account throughout the book. In particular, the Higgs decay channel into a pair of photons, which has played a crucial role in the discovery, is discussed.§As in the first edition, the accent is still on the semi-classical approximation. However, in view of the necessity of a discussion of H !, the authors give several indications about corrections to the semiclassical approximation. Violation of unitarity is discussed in more detail, including the dispersion relations as a tool for computing loop corrections; the above-mentioned Higgs decay channel is illustrated by means of a full one-loop calculation; and finally, loop effects on the production of unstable particles (such as the Z0 boson) are now discussed. Finally, the neutrino mass and oscillation analysis is updated taking into account the major achievements of the last years.§

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### Quantum Field Theory II Springer, Berlin

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This book takes a pedagogical approach§to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics.§§The first part of the book introduces quantum gravity, without§requiring previous knowledge of general relativity (GR). The necessary§geometrical aspects are derived afresh leading to explicit general Lagrangians§for gravity, including that of general relativity. The quantum aspect of§gravitation, as described by the graviton, is introduced and perturbative§quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute§the one-loop contribution to the theory and renormalizability aspects of the§perturbative theory are also discussed. This follows by introducing only the§very basics of a non-perturbative, background-independent, formulation of§quantum gravity, referred to as "loop quantum gravity", which gives rise to a§quantization of space.§§In the second part the author introduces supersymmetry and§its consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell's§Theory as well as of Yang-Mills field theory, and of the standard model are§worked out. Spontaneous symmetry breaking, improvement of the divergence§problem in supersymmetric field theory, and its role in the hierarchy problem§are covered. The unification of the fundamental constants in a supersymmetric§version of the standard model are then studied. Geometrical aspects necessary§to study supergravity are developed culminating in the derivation of its full§action.§§The third part§introduces string theory and the analysis of the spectra of the mass (squared)§operator associated with the oscillating strings. The properties of the§underlying fields, associated with massless particles, encountered in string§theory are studied in some detail. Elements of compactification, duality and§D-branes are given, as well of the generation of vertices and interactions of§strings. In the final sections, the author shows how to recover GR and the§Yang-Mills field Theory from string theory.§

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### Quantum Field Theory DOVER PUBLICATIONS

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Preface General References 1. Classical Theory 1.1 Principle of Least Action 1.1.1 Classical Motion 1.1.2 Electromagnetic Field as an Infinite Dynamical System 1.1.3 Electromagnetic Interaction of a Point Particle 1.2 Symmetries and Conservation Laws 1.2.1 Fundamental Invariants 1.2.2 Energy Momentum Tensor 1.2.3 Internal Symmetries 1.3 Propagation and Radiation 1.3.1 Green Functions 1.3.2 Radiation 2. The Dirac Equation 2.1 Toward a Relativistic Wave Equation 2.1.1 Quantum Mechanics and Relativity 2.1.2 The Dirac Equation 2.1.3 Relativistic Covariance 2.2 Physical Content 2.2.1 Plane Wave Solutions and Projectors 2.2.2 Wave Packets 2.2.3 Electromagnetic Coupling 2.2.4 Foldy-Wouthuysen Transformation 2.3 Hydrogen-like Atoms 2.3.1 Nonrelativistic versus Relativistic Spectrum 2.3.2 Dirac Theory 2.4 Hole Theory and Charge Conjugation 2.4.1 Reinterpretation of Negative Energy Solutions 2.4.2 Charge Conjugation 2.4.3 Zero-Mass Particles 2.5 Dirac Propagator 2.5.1 Free Propagator 2.5.2 Propagation in an Arbitrary External Electromagnetic Field 2.5.3 Application to the Coulomb Scattering 2.5.4 Fock-Schwinger Proper Time Method 3. Quantization--Free Fields 3.1 Canonical Quantization 3.1.1 General Formulation 3.1.2 Scalar Field 3.1.3 Charged Scalar Field 3.1.4 Time-Ordered Product 3.1.5 Thermodynamic Equilibrium 3.2 Quantized Radiation Field 3.2.1 Indefinite Metric 3.2.2 Propagator 3.2.3 Massive Vector Field 3.2.4 Vacuum Fluctuations 3.3 Dirac Field and Exclusion Principle 3.3.1 Anticommutators 3.3.2 Fock Space for Fermions 3.3.3 Relation between Spin and Statistics--Propagator 3.4 Discrete Symmetries 3.4.1 Parity 3.4.2 Charge Conjugation 3.4.3 Time Reversal 3.4.4 Summary 4. Interaction with an External Field 4.1 Quantized Electromagnetic Field Interacting with a Classical Source 4.1.1 Emission Probabilities 4.1.2 Emitted Energy and the Infrared Catastrophe 4.1.3 Induced Absorption and Emission 4.1.4 S Matrix and Evolution Operator 4.2 Wick's Theorem 4.2.1 Bose Fields 4.2.2 Fermi Fields 4.2.3 General Case 4.3 Quantized Dirac Field Interacting with a Classical Potential 4.3.1 General Formalism 4.3.2 Emission Rate to Lowest Order 4.3.3 Pair Creation in a Constant Uniform Electric Field 4.3.4 The Euler-Heisenberg Effective Lagrangian 5. Elementary Processes 5.1 S Matrix and Asymptotic Theory 5.1.1 Cross Sections 5.1.2 Asymptotic Theory 5.1.3 Reduction Formulas 5.1.4 Generating Functional 5.1.5 Connected Parts 5.1.6 Fermions 5.1.7 Photons 5.2 Applications 5.2.1 Compton Effect 5.2.2 Pair Annihilation 5.2.3 Positronium Lifetime 5.2.4 Bremsstrahlung 5.3 Unitarity and Causality 5.3.1 Unitarity and Partial Wave Decomposition 5.3.2 Causality and Analyticity 5.3.3 The Jost-Lehmann-Dyson Representation 5.3.4 Forward Dispersion Relations 5.3.5 Momentum Transfer Analyticity 6. Perturbation Theory 6.1 Interaction Representation and Feynman Rules 6.1.1 Self-Interacting Scalar Field 6.1.2 Feynman Rules for Spinor Electrodynamics 6.1.3 Electron-Electron and Electron-Positron Scattering 6.1.4 Scalar Electrodynamics 6.2 Diagrammatics 6.2.1 Loopwise Expansion 6.2.2 Truncated and Proper Diagrams 6.2.3 Parametric Representation 6.2.4 Euclidean Green Functions 6.3 Analyticity Properties 6.3.1 Landau Equations 6.3.2 Real Singularities 6.3.3 Real Singularities of Simple Diagrams 6.3.4 Physical-Region Singularities. Cutkosky Rules 7. Radiative Corrections 7.1 One-Loop Renormalization 7.1.1 Vacuum Polarization 7.1.2 Electron Propagator 7.1.3 Vertex Function 7.1.4 Summary 7.2 Radiative Corrections to the Interaction with an External Field 7.2.1 Effective Interaction and Anomalous Magnetic Moment 7.2.2 Radiative Corrections to Coulomb Scattering 7.2.3 Soft Bremsstrahlung 7.2.4 Finite Inclusive Cross Section 7.3 New Effects 7.3.1 Photon-Photon Scattering 7.3.2 Lamb Shift 7.3.3 Van der Waals Forces at Large Distances 8. Renormalization 8.1 Regularization and Power Counting 8.1.1 Introduction 8.1.2 Regularization 8.1.3 Power Counting 8.1.4 Convergence Theorem 8.2 Renormalization 8.2.1 Normalization Conditions and Structure of the Counterterms 8.2.2 Bogoliubov's Recursion Formula 8.2.3 Zimmermann's Explicit Solution 8.2.4 Renormalization in Parametric Space 8.2.5 Finite Renormalizations 8.2.6 Composite Operators 8.3 Zero-Mass Limit, Asymptotic Behavior, and Weinberg's Theorem 8.3.1 Massless Theories 8.3.2 Ultraviolet Behavior and Weinberg's Theorem 8.4 The Case of Quantum Electrodynamics 8.4.1 Formal Derivation of the Ward-Takahashi Identities 8.4.2 Pauli-Villars Regularization to All Orders 8.4.3 Renormalization 8.4.4 Two-Loop Vacuum Polarization 9. Functional Methods 9.1 Path Integrals 9.1.1 The Role of the Classical Action in Quantum Mechanics 9.1.2 Trajectories in the Bargmann-Fock Space 9.1.3 Fermion Systems 9.2 Relativistic Formulation 9.2.1 S Matrix and Green Functions in Terms of Path Integrals 9.2.2 Effective Action and Steepest-Descent Method 9.3 Constrained Systems 9.3.1 General Discussion 9.3.2 The Electromagnetic Field as an Example 9.4 Large Orders in Perturbation Theory 9.4.1 Introduction 9.4.2 Anharmonic Oscillator 10. Integral Equations and Bound-State Problems 10.1 The Dyson-Schwinger Equations 10.1.1 Field Equations 10.1.2 Renormalization 10.2 Relativistic Bound States 10.2.1 Homogeneous Bethe-Salpeter Equation 10.2.2 The Wick Rotation 10.2.3 Scalar Massless Exchange in the Ladder Approximation &n 12.3 The Effective Action at the One-Loop Order 12.3.1 General Form 12.3.2 Two-Point Function 12.3.3 Other Functions 12.3.4 One-Loop Renormalization 12.4 Renormalization 12.4.1 Slavnov-Taylor Identities 12.4.2 Identities for Proper Functions 12.4.3 Recursive Construction of the Counterterms 12.4.4 Gauge Dependence of Green Functions 12.4.5 Anomalies 12.5 Massive Gauge Fields 12.5.1 Historical Background 12.5.2 Massive Gauge Theory 12.5.3 Spontaneous Symmetry Breaking 12.5.4 Renormalization of Spontaneously Broken Gauge 12.5.5 Gauge Independence and Unitarity of the S Matrix 12.6 The Weinberg-Salam Model 12.6.1 The Model for Leptons 12.6.2 Electron-Neutrino Cross Sections 12.6.3 Higher-Order Corrections 12.6.4 Incorporation of Hadrons 13. Asymptotic Behavior 13.1 Effective Charge in Electrodynamics 13.1.1 The Gell-Mann and Low Function 13.1.2 The Callan-Symanzik Equation 13.2 Broken Scale Invariance 13.2.1 Scale and Conformal Invariance 13.2.2 Modified Ward Identities 13.2.3 Callan-Symanzik Coefficients to Lowest Order 13.3 Scale Invariance Recovered 13.3.1 Coupling Constant Flow 13.3.2 Asymptotic Freedom 13.3.3 Mass Corrections 13.4 Deep Inelastic Lepton-Hadron Scattering and Electron-Positron Annihilation into Hadrons 13.4.1 Electroproduction 13.4.2 Light-Cone Dynamics 13.4.3 Electron-Positron Annihilation 13.5 Operator Product Expansions 13.5.1 Short-Distance Expansion 13.5.2 Dominant and Subdominant Operators, Operator Mixing, and Conservation Laws 13.5.3 Light-Cone Expansion Appendix A-1 Metric A-2 Dirac Matrices and Spinors A-3 Normalization of States, S Matrix, Unitarity, and Cross Sections A-4 Feynman Rules Index

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### Relativistic Cosmology Cambridge University Press

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Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

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### Quantum Physics in the Nanoworld Springer, Berlin

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The second edition deals with all essential aspects of non-relativistic quantum physics up to the quantisation of fields. In contrast to common textbooks of quantum mechanics, modern experiments are described both for the purpose of foundation of the theory and in relation to recent applications. Links are made to important research fields and applications such as elementary particle physics, solid state physics and nuclear magnetic resonance in medicine, biology and material science. Special emphasis is paid to quantum physics in nanoelectronics such as resonant tunnelling, Coulomb blockade and the realisation of quantum bits.§This second edition also considers quantum transport through quantum point contacts and its application as charge detectors in nanoelectronic circuits. Because of its recent interest a brief discussion of Bose-Einstein condensation has been included, as well as the recently detected Higgs particle. Another essential new addition to the present book concerns a detailed discussion of the particle picture in quantum field theory. Counterintuitive aspects of single particle quantum physics such as particle-wave duality and the Einstein-Podolski-Rosen (EPR) paradox appear more acceptable to our understanding if discussed on the background of quantum field theory. The non-locality of quantum fields explains non-local behaviour of particles in classical Schrödinger quantum mechanics. Finally, new problems have been added.§The book is suitable as an introduction into quantum physics, not only for physicists but also for chemists, biologists, engineers, computer scientists and even for philosophers as far as they are interested in natural philosophy and epistemology.

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### Quantum Mechanics Dover Publications

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"Strongly recommended" by the American Journal of Physics, this volume serves as a text for advanced undergraduates and graduate students of physics as well as a reference for professionals. Clear in its presentation and scrupulous in its attention to detail, the treatment originally appeared in a two-volume French edition. This convenient single-volume translation begins with formalism and its interpretation, starting with the origins of quantum theory and examinations of matter waves and the Schrödinger equation, one-dimensional quantized systems, the uncertainty relations, and the mathematical framework and physical content of formalism. The second half opens with an exploration of symmetries and invariance, including a consideration of angular momentum, identical particles and the Pauli exclusion principle, invariance and conservation laws, and time reversal. Methods of approximation include those involving stationary perturbations, the equation of motion, variational method, and collision theory. The final chapters review the elements of relativistic quantum mechanics, and each of the two volumes concludes with useful appendixes. Reprint of the John Wiley & Sons, New York, two-volume 1958 edition.

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### Quantum Mechanics Nova Science Publishers Inc

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The book Quantum Mechanics: Principles, New Perspectives, Extensions and Interpretation Revised Edition deals with the foundations of Quantum Mechanics in a quite novel way. From his own published works throughout these last 20 years in prominent Journals, Prof. L.S.F. Olavo reconstructs Quantum Mechanics (as related to the Schrdinger equation) from the scratch, both in mathematical and interpretive ways. The picture that emerges is quite different from the one we get from other approaches. While the mainstream approach reinforces some unavoidable weirdness in the Quantum World, Prof. Olavos interpretation presents Quantum Mechanics as quite an intuitive theory, using only the pedestrian notions of randomness, fluctuations and the companion notion of statistics. However, it is much more than another stochastic approach. Throughout the first part of the book, Prof. Olavo shows how the various roads to derive the Schrdinger equation can be reduced to his own mathematical construction: Feynmans path integral and the stochastic approach are but two of them. The book also brings about quite new results, such as the connection between Quantum Mechanics and the Central Limit Theorem and Langevin Equations (by means of which quantum phenomena can be easily simulated and make visualizable). All this is done taking recourse to only three axioms. This strategy gives the book an impressive power of synthesis in what respects the interpretation of the formalism. In fact, in the last part of the book, Prof. Olavo shows how some of the innumerous proposals for the interpretation of Quantum Mechanics, with some of their constructs, can help us making a rational reconstruction of a Quantum World without any weirdness whatsoever. In the second part, to remove some of the various obstacles to a Quantum Mechanics without weirdness, the book deals with the most prominent aspects and experiments of the Quantum, such as spin and the Stern-Gerlach experiment, the construction of operators and also Identical Particles. In the third part, the book presents a fully special and general relativistic extension of the formalism by just making the extension of the three postulates used throughout the first part. This book is intended to all those interested in the foundations of Quantum Mechanics.

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### Elementary Theory of Angular Momentum Dover Publications

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Part A. GENERAL THEORY I. REVIEW OF BASIC PRINCIPLES 1. HERMITIAN OPERATORS 2. UNITARY TRANSFORMATIONS 3. DIAGONALIZATION OF OPERATORS 4. EXPONENTIAL FORM OF THE UNITARY OPERATORS II. THE ANGULAR MOMENTUM OPERATORS 5. DEFINITION OF ANGULAR MOMENTUM OPERATORS 6. ORBITAL ANGULAR MOMENTUM 7. COMMUTATION RULES FOR ANGULAR MOMENTUM OPERATORS 8. EIGENVALUES OF THE ANGULAR MOMENTUM OPERATORS 9. PHYSICAL INTERPRETATION OF ANGULAR MOMENTUM III. COUPLING OF TWO ANGULAR MOMENTA 10. DEFINITION OF THE CLEBSCH-GORDAN COEFFICIENTS 11. SYMMETRY RELATIONS OF THE CLEBSCH-GORDAN COEFFICIENTS 12. EVALUATION OF CLEBSCH-GORDAN COEFFICIENTS IV. TRANSFORMATION PROPERTIES UNDER ROTATIONS 13. MATRIX REPRESENTATIONS OF THE ROTATION OPERATORS 14. THE CLEBSCH-GORDAN SERIES 15. DETERMINATION OF THE ROTATION MATRICES 16. ORTHOGONALITY AND NORMALIZATION OF THE ROTATION MATRICES V. IRREDUCIBLE TENSORS 17. DEFINITION OF IRREDUCIBLE TENSOR OPERATORS 18. RACAH'S DEFINITION OF IRREDUCIBLE TENSOR OPERATORS 19. THE WIGNER-ECKART THEOREM 20. THE PROJECTION THEOREM FOR FIRST-RANK TENSORS 21. ANGULAR MOMENTUM OF A VECTOR FIELD VI. RACAH COEFFICIENTS 22. COUPLING OF THREE ANGULAR MOMENTA 23. PROPERTIES OF THE RACAH COEFFICIENTS 24. BASIC APPLICATIONS 25. THE GRADIENT FORMULA Part B. APPLICATIONS VII. THE ELECTROMAGNETIC FIELD 26. THE MAXWELL EQUATIONS 27. THE MULTIPOLE FIELDS VIII. STATIC INTERACTIONS 28. MULTIPOLE MOMENTS OF AN ELECTROSTATIC CHARGE DISTRIBUTION 29. SPIN INTERACTIONS IX. PARTICLES OF SPIN 1/2 30. NON-RELATIVISTIC DESCRIPTION 31. RELATIVISTIC DESCRIPTION X. ORIENTED NUCLEI AND ANGULAR CORRELATIONS 32. CAPTURE OF POLARIZED NEUTRONS BY POLARIZED NUCLEI 33. ANGULAR CORRELATION 34. EMISSION OF ALPHA PARTICLES BY AN ORIENTED NUCLEUS XI. ANGULAR DISTRIBUTIONS IN NUCLEAR REACTIONS 35. j-j AND L-S COUPLING 36. ANGULAR MOMENTUM COUPLING IN NUCLEAR REACTIONS XII. IDENTICAL PARTICLES 37. IDENTICAL PARTICLES IN j-j COUPLING 38. IDENTICAL PARTICLES IN L-S COUPLING 39. THE ISOTOPIC SPIN APPENDIX I. CLEBSCH-GORDAN AND RACAH COEFFICIENTS APPENDIX II. THE ROTATION MATRICES APPENDIX III. THE SPHERICAL HARMONICS AUTHOR INDEX SUBJECT INDEX

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### Field Theory Handbook Springer, Berlin

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Let us first state exactly what this book is and what it is not. It is a compendium of equations for the physicist and the engineer working with electrostatics, magne tostatics, electric currents, electromagnetic fields, heat flow, gravitation, diffusion, optics, or acoustics. It tabulates the properties of 40 coordinate systems, states the Laplace and Helmholtz equations in each coordinate system, and gives the separation equations and their solutions. But it is not a textbook and it does not cover relativistic and quantum phenomena. The history of classical physics may be regarded as an interplay between two ideas, the concept of action-at-a-distance and the concept of a field. Newton's equation of universal gravitation, for instance, implies action-at-a-distance. The same form of equation was employed by COULOMB to express the force between charged particles. AMPERE and GAUSS extended this idea to the phenomenological action between currents. In 1867, LUDVIG LORENZ formulated electrodynamics as retarded action-at-a-distance. At almost the same time, MAXWELL presented the alternative formulation in terms of fields. In most cases, the field approach has shown itself to be the more powerful.

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### Charged Particle Traps II Springer, Berlin

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This is the second volume of Charged Particle Traps devoted to applications, complementing the first volume s comprehensive treatment of the theory and practice of charged particle traps, their many variants and refinements. In recent years, applications of far reaching importance have emerged ranging from the ultra-precise mass determinations of elementary particles and their antiparticles and short-lived isotopes, to high-resolution Zeeman spectroscopy on multiply-charged ions, to microwave and optical spectroscopy, some involving "forbidden" transitions from metastable states of such high resolution that optical frequency standards are realized by locking lasers to them. Further the potential application of trapped ions to quantum computing is explored, based on the extraordinary quantum state coherence made possible by the particle isolation. Consideration is given to the Paul and Penning traps as potential quantum information processors.

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### Feynman's Thesis World Scientific Publishing Co Pte Ltd

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Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled "The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space-time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure. The result was the path integral approach, which satisfied - and transcended - its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space-time viewpoint. The present volume includes Feynman's Princeton thesis, the related review article "Space-Time Approach to Non-Relativistic Quantum Mechanics" ["Reviews of Modern Physics" 20 (1948), 367- 387], Paul Dirac's seminal paper "The Lagrangian in Quantum Mechanics'' ["Physikalische Zeitschrift der Sowjetunion", Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.

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