Mathematical Theory Of Quantum Fields
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| Author | : Huzihiro Araki |
| Publisher | : Oxford University Press |
| Total Pages | : 254 |
| Release | : 1999-10-22 |
| Genre | : Science |
| ISBN | : 0192539116 |
This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.
| Author | : Asao Arai |
| Publisher | : World Scientific |
| Total Pages | : 1115 |
| Release | : 2024-09-03 |
| Genre | : Mathematics |
| ISBN | : 9811288453 |
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.
| Author | : Huzihiro Araki |
| Publisher | : OUP Oxford |
| Total Pages | : 254 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0198517734 |
Quantum field theory is an area of wide and growing interest to students and researchers of both mathematics and physics. This text is an introduction to the subject which uses mathematical theory of operator algebras to present the theory.
| Author | : Albert Schwarz |
| Publisher | : World Scientific |
| Total Pages | : 461 |
| Release | : 2020-04-15 |
| Genre | : Science |
| ISBN | : 981327865X |
The book is very different from other books devoted to quantum field theory, both in the style of exposition and in the choice of topics. Written for both mathematicians and physicists, the author explains the theoretical formulation with a mixture of rigorous proofs and heuristic arguments; references are given for those who are looking for more details. The author is also careful to avoid ambiguous definitions and statements that can be found in some physics textbooks.In terms of topics, almost all other books are devoted to relativistic quantum field theory, conversely this book is concentrated on the material that does not depend on the assumptions of Lorentz-invariance and/or locality. It contains also a chapter discussing application of methods of quantum field theory to statistical physics, in particular to the derivation of the diagram techniques that appear in thermo-field dynamics and Keldysh formalism. It is not assumed that the reader is familiar with quantum mechanics; the book contains a short introduction to quantum mechanics for mathematicians and an appendix devoted to some mathematical facts used in the book.
| Author | : Frédéric Paugam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 485 |
| Release | : 2014-02-20 |
| Genre | : Science |
| ISBN | : 3319045644 |
This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.
| Author | : Jonathan Dimock |
| Publisher | : Cambridge University Press |
| Total Pages | : 239 |
| Release | : 2011-02-03 |
| Genre | : Science |
| ISBN | : 1139497480 |
Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.
| Author | : Istvan Montvay |
| Publisher | : Cambridge University Press |
| Total Pages | : 512 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780521599177 |
Presents a comprehensive and coherent account of the theory of quantum fields on a lattice.
| Author | : Gerald B. Folland |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 325 |
| Release | : 2021-02-03 |
| Genre | : Education |
| ISBN | : 1470464837 |
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.
| Author | : Pierre Deligne |
| Publisher | : American Mathematical Society |
| Total Pages | : 801 |
| Release | : 1999-10-25 |
| Genre | : Mathematics |
| ISBN | : 0821820133 |
A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
| Author | : Edson de Faria |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2010-08-12 |
| Genre | : Science |
| ISBN | : 1139489801 |
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
