Download or read book Quantum Field Theory written by G. B. Folland and published by American Mathematical Soc.. This book was released on 2008-08-26 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Field Theory A Tourist Guide for Mathematicians written by Gerald B. Folland and published by American Mathematical Soc.. This book was released on 2021-02-03 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Theory for Mathematicians written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2013-06-19 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Download or read book Modern Quantum Field Theory written by Tom Banks and published by Cambridge University Press. This book was released on 2008-09-18 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.
Download or read book Introduction To String Field Theory written by Warren Siegel and published by World Scientific. This book was released on 1988-09-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the most up-to-date findings on string field theory. It is presented in a new approach as a result of insights gained from the theory. This includes the use of a universal method for treating free field theories, which allows the derivation of a single, simple, free, local, Poincare-invariant, gauge-invariant action that can be applied directly to any fields.
Download or read book Renormalization and Effective Field Theory written by Kevin Costello and published by American Mathematical Soc.. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Field Theory for Mathematicians written by Robin Ticciati and published by Cambridge University Press. This book was released on 1999-06-13 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: This should be a useful reference for anybody with an interest in quantum theory.
Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Download or read book Quantum Field Theory in a Nutshell written by Anthony Zee and published by Princeton University Press. This book was released on 2010-02-01 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University
Download or read book Methods of Contemporary Gauge Theory written by Yuri Makeenko and published by Cambridge University Press. This book was released on 2023-07-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Field Theory for the Gifted Amateur written by Tom Lancaster and published by Oxford University Press. This book was released on 2014-04 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory provides the theoretical backbone to most modern physics. This book is designed to bring quantum field theory to a wider audience of physicists. It is packed with worked examples, witty diagrams, and applications intended to introduce a new audience to this revolutionary theory.
Download or read book Vector Analysis written by N. Kemmer and published by CUP Archive. This book was released on 1977-01-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to the treatment of time-dependent integrals over fields - is achieved by the introduction from the outset of a method of general parametrisation of curves and surfaces.
Download or read book Quantum Field Theory Batalin Vilkovisky Formalism and Its Applications written by Pavel Mnev and published by American Mathematical Soc.. This book was released on 2019-08-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.
Download or read book Fundamental Mathematical Structures of Quantum Theory written by Valter Moretti and published by Springer. This book was released on 2019-06-20 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.
Download or read book Quantum Field Theory and the Standard Model written by Matthew D. Schwartz and published by Cambridge University Press. This book was released on 2014 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.
Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
