Quantum Field Theory A Tourist Guide For Mathematicians
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Author | : Gerald B. Folland |
Publisher | : American Mathematical Soc. |
Total Pages | : 325 |
Release | : 2021-02-03 |
Genre | : Education |
ISBN | : 1470464837 |
Download Quantum Field Theory: A Tourist Guide for Mathematicians Book in PDF, Epub and Kindle
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 | : G. B. Folland |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 2008-08-26 |
Genre | : Mathematics |
ISBN | : 0821847058 |
Download Quantum Field Theory Book in PDF, Epub and Kindle
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 | : Brian C. Hall |
Publisher | : Springer Science & Business Media |
Total Pages | : 566 |
Release | : 2013-06-19 |
Genre | : Science |
ISBN | : 1461471168 |
Download Quantum Theory for Mathematicians Book in PDF, Epub and Kindle
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.
Author | : Tom Banks |
Publisher | : Cambridge University Press |
Total Pages | : 323 |
Release | : 2008-09-18 |
Genre | : Science |
ISBN | : 1139473891 |
Download Modern Quantum Field Theory Book in PDF, Epub and Kindle
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.
Author | : Michael Stone |
Publisher | : Cambridge University Press |
Total Pages | : 821 |
Release | : 2009-07-09 |
Genre | : Science |
ISBN | : 1139480618 |
Download Mathematics for Physics Book in PDF, Epub and Kindle
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.
Author | : Robin Ticciati |
Publisher | : Cambridge University Press |
Total Pages | : 720 |
Release | : 1999-06-13 |
Genre | : Mathematics |
ISBN | : 052163265X |
Download Quantum Field Theory for Mathematicians Book in PDF, Epub and Kindle
This should be a useful reference for anybody with an interest in quantum theory.
Author | : Kevin Costello |
Publisher | : American Mathematical Soc. |
Total Pages | : 264 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821852884 |
Download Renormalization and Effective Field Theory Book in PDF, Epub and Kindle
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.
Author | : Warren Siegel |
Publisher | : World Scientific |
Total Pages | : 256 |
Release | : 1988-09-01 |
Genre | : Science |
ISBN | : 9814507458 |
Download Introduction To String Field Theory Book in PDF, Epub and Kindle
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.
Author | : Tom Lancaster |
Publisher | : Oxford University Press |
Total Pages | : 505 |
Release | : 2014-04 |
Genre | : Science |
ISBN | : 0199699321 |
Download Quantum Field Theory for the Gifted Amateur Book in PDF, Epub and Kindle
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.
Author | : Michael Spivak |
Publisher | : |
Total Pages | : 733 |
Release | : 2010 |
Genre | : Mechanics |
ISBN | : 9780914098324 |
Download Physics for Mathematicians Book in PDF, Epub and Kindle