Designed for self-study or advanced courses in relativity and quantum field theory, this introduction arose from a graduate level course and assumes some knowledge of general relativity and differential geometry.

Few words about quantum field theory.

To establish the setting of this presentation, consider as an example the classic problem of a scalar field in a box. More precisely, consider a “Casimir slab” of width L in 4-dimensional space-time, with the energy-momentum tensor associated with minimal gravitational coupling. With the spatial operator in the field equation, H = ?? 2, several quantities are associated:

We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold.Показать полностьюWe start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior.

Gauge field theories underlie all models now used in elementary particle physics. These theories refer to the class of singular theories which are also theories with constraints.Показать полностьюGauge field theories underlie all models now used in elementary particle physics. These theories refer to the class of singular theories which are also theories with constraints. The quantization of singular theories remains one of the key problems of quantum field theory and is being intensively discussed in the literature. This book is an attempt to fill the need for a comprehensive analysis of this problem, which has not heretofore been met by the available monographs and reviews. The main topics are canonical quantization and the path integral method. In addition, the Lagrangian BRST quantization is completely described, for the first time in monograph. The book also represents a number of original results obtained by the authors, in particular, a complete description of the physical sector of an arbitrary gauge theory, quantization of singuar theories with higher derivatives, quantization of theories with time-dependent constraints, and correct canonical quantization of theories of a relativistic point-like particle. As a general illustration we present quantization of field theories such as electrodynamics, Yang-Mills theory, and gravity.

The second volume of this authoritative work traces the material outlined in the first, but in far greater detail and with a much higher degree of sophistication.Показать полностьюThe second volume of this authoritative work traces the material outlined in the first, but in far greater detail and with a much higher degree of sophistication. The authors begin with the theory of the electromagnetic interaction, and then consider hadronic structure, exploring the accuracy of the quark model by examining the excited states of baryons and mesons. They introduce the color variable as a prelude to the development of quantum chromodynamics, the theory of the strong interaction, and go on to discuss the electroweak interaction — the broken symmetry of which they explain by the Higgs mechanism — and conclude with a consideration of grand unification theories.

The present work — and its two companion volumes — will certainly be among the most effective and widely used ... Can be warmly recommended to all nuclear physicists, student and professional alike, who have an interest in mechanisms of nuclear excitation...

The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet there is much more involved than just a basic set of equations which eventually has to be solved when applied to specific problems.Показать полностьюThe fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet there is much more involved than just a basic set of equations which eventually has to be solved when applied to specific problems. We have learned in recent years that the structure of the ground state of field theories (with which we are generally concerned) plays an equally funda- fundamental role as the equations of motion themselves. Heisenberg was probably the first to recognize that the ground state, the vacuum, could acquire certain properties (quantum numbers) when he devised a theory of ferromagnetism. Since then, many more such examples are known in solid state physics, e. g. superconductivity, superfluidity, in fact all problems concerned with phase transitions of many-body systems, which are often summarized under the name synergetics.

Field Quantization is a thorough introduction to the physical ideas and techniques of this subject, starting from an elementary level. The initial chapters deal with the quantum mechanics of systems having many degrees of freedom and with classical Lagrangian field theory.Показать полностьюField Quantization is a thorough introduction to the physical ideas and techniques of this subject, starting from an elementary level. The initial chapters deal with the quantum mechanics of systems having many degrees of freedom and with classical Lagrangian field theory. Subsequently, both the traditional method of canonical quantization and the modern approach using path integrals are studied. The material is presented in considerable detail and accompanied by a large number of worked examples and exercises.

This completely revised and corrected new edition provides several new examples and exercises to enable deeper insight in formalism and application of Quantum electrodynamics.Показать полностьюThis completely revised and corrected new edition provides several new examples and exercises to enable deeper insight in formalism and application of Quantum electrodynamics. It is a thorough introductory text providing all necessary mathematical tools together with many examples and worked problems. In their presentation of the subject the authors adopt a heuristic approach based on the propagator formalism. The latter is introduced in the first two chapters in both its nonrelativistic and relativistic versions. Subsequently, a large number of scattering and radiation processes involving electrons, positrons, and photons are introduced and their theoretical treatment is presented in great detail. Higher order processes and renormalization are also included. The book concludes with a discussion of two-particle states and the interaction of spinless bosons.

More than a generation of German-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modern theoretical physics - with mathematics, the most funda- mental of sciences - using Walter Greiner's textbooks as their guide.Показать полностьюMore than a generation of German-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modern theoretical physics - with mathematics, the most funda- mental of sciences - using Walter Greiner's textbooks as their guide. The idea of developing a coherent, complete presentation of an entire field of science in a series of closely related textbooks is not a new one. Many older physicists remember with real pleasure their sense of adventure and discovery as they worked their ways through the classic series by Sommerfeld, by Planck and by Landau and Lifshitz. From the students' viewpoint, there are a great many obvious advantages to be gained through use of consistent notation, logical ordering of topics and coherence of presentation; beyond this, the complete coverage of the science provides a unique opportunity for the author to convey his personal enthusiasm and love for his subject. The present five-volume set, Theoretical Physics, is in fact only that part of the complete set of textbooks developed by Greiner and his students that presents the quantum theory. I have long urged him to' make the remaining vol- umes on classical mechanics and dynamics, on electromagnetism, on nuclear and particle physics, and on special topics available to an English-speaking audience as well, and we can hope for these companion volumes covering all of theoretical physics some time in the future. What makes Greiner's volumes of particular value to the student and professor alike is their completeness. Greiner avoids the all too common "it follows that ..." which conceals several pages of mathematical manipulation and confounds the student. He does not hesitate to include experimental data to illuminate or illustrate a theoretical point and these data, like the theoret- ical content, have been kept up to date and topical through frequent revision and expansion of the lecture notes upon which these volumes are based. Moreover, Greiner greatly increases the value of his presentation by includ- ing something like one hundred completely worked examples in each volume. Nothing is of greater importance to the student than seeing, in detail, how the theoretical concepts and tools under study are applied to actual problems of interest to a working physicist. And, finally, Greiner adds brief biographical sketches to each chapter covering the people responsible for the development of the theoretical ideas and/or the experimental data presented. It was Auguste Comte (1798-1857) in his Positive Philosophy who noted, "To understand a science it is necessary to know its history". This is all too often forgotten in modern physics teaching and the bridges that Greiner builds to the pioneering figures of our science upon whose work we build are welcome ones. Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.

This is the first quantitative treatment of elementary particle theory that is accessible to undergraduates. Using a lively, informal writing style, the author strikes a balance between quantitative rigor and intuitive understanding.

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals.Показать полностьюThe Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

We shall start our study of quantum field theory with a review of classical dynamics and classical field theory, with emphasis on those aspects that will prove important in the quantization of the theory.Показать полностьюWe shall start our study of quantum field theory with a review of classical dynamics and classical field theory, with emphasis on those aspects that will prove important in the quantization of the theory. These include the action principle, the Lagrangian and Hamiltonian formulations of classical dynamics, the structure of phase space and Poisson brackets, and the significance of canonical transformations.

This book gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach, it describes both the physical concepts and the mathematical structures and their consequences.Показать полностьюThis book gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach, it describes both the physical concepts and the mathematical structures and their consequences. These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, the analysis of possible charge structures, and exchange symmetries including braid group statistics. Thermal states of an unbounded medium and local equilibrium are discussed in detail. The author takes care both to describe the ideas and to give a critical assessment of future perspectives. The new edition contains numerous improvements and a new chapter concerning formalism and interpretation of quantum theory.

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings.Показать полностьюThe purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.

There is another aspect that needs emphasis. From the outset the canonical operator formalism is not a perturbation theory, while diagrams certainly are perturbative objects.Показать полностьюThere is another aspect that needs emphasis. From the outset the canonical operator formalism is not a perturbation theory, while diagrams certainly are perturbative objects. Using diagrams as a starting point seems therefore to be a capitulation in the struggle to go beyond perturbation theory. It is unthinkable to accept as a final goal a perturbation theory, and it is not our purpose to forward such a notion. On the contrary, it becomes more and more clear that perturbation theory is a very useful device to discover equations and properties that may hold true even if the perturbation expansion fails. There are already several examples of this mechanism: on the simplest level there is for instance the treatment of unstable particles, while if it comes to unfathomed depths the Callan-Symanzik equation may be quoted. All such treatments have in common that global properties are established for diagrams and then extrapolated beyond perturbation theory. Global properties are those that hold in arbitrary order of perturbation theory for the grand total of all diagrams entering at any given order. It is here that very naturally the concept of the global diagram enters: it is for a given order of perturbation theory, for a given number of external lines the sum of all contributing diagrams. This object, very often presented as a blob, an empty circle, in the following pages, is supposed to have a significance beyond perturbation theory. Practically all equations of the canonical formalism can be rewritten in terms of such global diagrams, thereby opening up the arsenal of the canonical formalism for this approach.

The purpose of this paper is to present a new manifestly conformally covariant formalism for the treatment of spinor fields in flat space-time. The formalism is especially well-suited for the analysis of the global complex analytic and asymptotic properties of fields.Показать полностьюThe purpose of this paper is to present a new manifestly conformally covariant formalism for the treatment of spinor fields in flat space-time. The formalism is especially well-suited for the analysis of the global complex analytic and asymptotic properties of fields. Our approach is developed within the framework of complex projective geometry, and is intimately related to the theory of twistors.

I chose for this book descriptions of my favorite work in mathematical physics, and I thank Dr. К. К. Phua for giving me the occasion to recollect this material.Показать полностьюI chose for this book descriptions of my favorite work in mathematical physics, and I thank Dr. К. К. Phua for giving me the occasion to recollect this material. Also I took this opportunity to publicize once again topics that fascinate me but have not yet resonated strongly with the public: for example, classical sources in Yang-Mills theory and mean field descriptions of non-equilibrium processes. Texts were edited only lightly: blatant missteps were corrected, but there remains plenty evidence of my wondering in the dark.

There is also a third framework within which quantum field theory may be studied: the functional Schrodinger picture. Although well-known, at least for boson fields, it has not been used as widely as the previous two methods, presumably because its intrinsically Lorentz non-covariant structure makes perturbative renormalized calculation difficult, though the renormalizability of this approach has been established by Symanzik in his last paper.1