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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.
Preface
List of Notation
Introduction
Chapter I Group of Symmetry of Elementary Particles
Chapter II Classical Theory of the Free Fields
Chapter III Classical Theory of the Interacting Fields
Chapter IV Second Quantization of Fields
Chapter V Quantum Theory of Interacting Fields. General Problems
Chapter VI Axiomatic and Euclidean Field Theory
Chapter VII Quantum Theory of Gauge Fields
Instructions to Problems of Chapters I to VII
References
Index