Quantum Theory for Mathematicians
Title | Quantum Theory for Mathematicians PDF eBook |
Author | Brian C. Hall |
Publisher | Springer Science & Business Media |
Total Pages | 566 |
Release | 2013-06-19 |
Genre | Science |
ISBN | 1461471168 |
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.
Quantum Theory for Mathematicians
Title | Quantum Theory for Mathematicians PDF eBook |
Author | Brian C. Hall |
Publisher | |
Total Pages | 554 |
Release | 2016 |
Genre | Quantum theory |
ISBN | 9787519203238 |
Quantum Mechanics for Mathematicians
Title | Quantum Mechanics for Mathematicians PDF eBook |
Author | Leon Armenovich Takhtadzhi͡an |
Publisher | American Mathematical Soc. |
Total Pages | 410 |
Release | 2008 |
Genre | Mathematics |
ISBN | 0821846302 |
Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.
Lectures on Quantum Mechanics for Mathematics Students
Title | Lectures on Quantum Mechanics for Mathematics Students PDF eBook |
Author | L. D. Faddeev |
Publisher | American Mathematical Soc. |
Total Pages | 250 |
Release | 2009 |
Genre | Quantum theory |
ISBN | 082184699X |
Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
Quantum Fields and Strings: A Course for Mathematicians
Title | Quantum Fields and Strings: A Course for Mathematicians PDF eBook |
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.
Quantum Theory
Title | Quantum Theory PDF eBook |
Author | Peter Bongaarts |
Publisher | Springer |
Total Pages | 460 |
Release | 2014-12-01 |
Genre | Science |
ISBN | 3319095617 |
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
Quantum Field Theory: A Tourist Guide for Mathematicians
Title | Quantum Field Theory: A Tourist Guide for Mathematicians PDF eBook |
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.