This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.

Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

A concise, beginner-friendly introduction to quantum field theory Quantum field theory is a powerful framework that extends quantum mechanics in ways that are essential in many modern applications. While it is the fundamental formalism for the study of many areas of physics, quantum field theory requires a different way of thinking, and many newcomers to the subject struggle with the transition from quantum mechanics. A Prelude to Quantum Field Theory introduces the key concepts of quantum field theory in a brief and accessible manner while never sacrificing mathematical rigor. The result is an easy-to-use textbook that distills the most general properties of the theory without overwhelming beginning students with more advanced applications. Bridges quantum mechanics and quantum field theory, emphasizing analogies and differences Emphasizes a “quantum field theoretical mindset” while maintaining mathematical rigor Obtains quantum fields as the continuum limit of a quantized system of many particles Highlights the correspondence between wave function—fundamental in quantum mechanics—and the formalism of second quantization used in quantum field theory Provides a step-by-step derivation of Feynman rules for the perturbative study of interacting theories Introduces students to renormalization, path integrals techniques, and more Discusses more modern topics like effective field theories Ideal for both undergraduate and graduate students Proven in the classroom

Modern physics is characterized by two great theories, which make it fundamentally different from its predecessor: quantum theory and theory of relativity. In this book we want to bring to the reader's attention several solutions to problems connected to the quantum-relativistic interaction of particles. Remarkably, such solutions furnished rigorous and pertinent explanations of a large set of phenomena, both in microscopic world and galactic universe. Contents: PrefaceIntroductionClassical and Quantum Free FieldsThe Gravitational Transmutations HypothesisTomonaga–Schwinger Representation of Dynamics of a Quantum Physical System. Matrix Elements of the Field Operators and Feynman{Dyson-Type Rules for High-Spin ParticlesFundamentals of Gauge Theories. The Minimal Coupling PrincipleThe Gravitational Field Interacting with Other FieldsInteraction of Scalar, Spinorial, Spin-Vectorial and Tensorial Particles, and the Gravitational Field Described by the Schwarzschild MetricScattering of Electrons and Photogeneration of Gravitons in External Gravitational FieldInteraction of Scalar, Spinorial, Vectorial, Spin-Vectorial and Tensorial Particles with the Axially-Symmetric Gravitational Field Described by the Kerr MetricSoftware Package for Analytical Calculation of Differential Cross-Sections of Gravitational Scattering of High-Spin ParticlesAppendices: Isotopic FormalismThe Dirac Matrices and the Dirac EquationOperatorial TransformationsSingular FunctionsIntegration Formulas in Momentum SpaceMatrix Elements of the Field Operators and First-Order Vertices for the Gravitational Interaction of ParticlesExpressions of the Coeffcients-Functions of the Differential and Integral Scattering Cross-Sections of Particles in the External Axially-Symmetric Gravitational Field Described by the Kerr MetricValues of Several Physical Quantities in CGS and Natural (ħ = 1, c = 1) Unit Systems. Equivalence Between Different Units of Measurement Readership: Researchers and graduate students in quantum field theory and theoretical physics. Keywords: Quantum FieldsReview: Key Features: In this book we present several solutions to problems connected to the quantum-relativistic interaction of particles. Remarkably, such solutions furnished rigorous and pertinent explanations of a large set of phenomena, both in microscopic world and universe

This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.