Lie Groups and Quantum Mechanics
| Author | : D. J. Simms |
| Publisher | : Springer |
| Total Pages | : 98 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540358293 |
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Classical and Quantum Mechanics with Lie Algebras
| Author | : Yair Shapira |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 600 |
| Release | : 2021 |
| Genre | : Science |
| ISBN | : 9789811241451 |
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How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics. Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle. Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise. The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics.
Quantum Theory, Groups and Representations
| Author | : Peter Woit |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2017-11-01 |
| Genre | : Science |
| ISBN | : 3319646125 |
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This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Quantum Theory for Mathematicians
| Author | : Brian C. Hall |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 566 |
| Release | : 2013-06-19 |
| Genre | : Science |
| ISBN | : 1461471168 |
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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 Lie Theory
| Author | : Vladislav Kharchenko |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2015-12-25 |
| Genre | : Mathematics |
| ISBN | : 9783319227030 |
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This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Lie Algebras In Particle Physics
| Author | : Howard Georgi |
| Publisher | : Westview Press |
| Total Pages | : 340 |
| Release | : 1999-10-22 |
| Genre | : Science |
| ISBN | : 0738202339 |
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An exciting new edition of a classic text
Affine Lie Algebras and Quantum Groups
| Author | : Jürgen Fuchs |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 1995-03-09 |
| Genre | : Mathematics |
| ISBN | : 9780521484121 |
Download Affine Lie Algebras and Quantum Groups Book in PDF, ePub and Kindle
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
Lie Groups, Physics, and Geometry
| Author | : Robert Gilmore |
| Publisher | : Cambridge University Press |
| Total Pages | : 5 |
| Release | : 2008-01-17 |
| Genre | : Science |
| ISBN | : 113946907X |
Download Lie Groups, Physics, and Geometry Book in PDF, ePub and Kindle
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Semi-Simple Lie Algebras and Their Representations
| Author | : Robert N. Cahn |
| Publisher | : Courier Corporation |
| Total Pages | : 180 |
| Release | : 2014-06-10 |
| Genre | : Mathematics |
| ISBN | : 0486150313 |
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Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.
Lie Algebras and Quantum Mechanics
| Author | : Robert Hermann |
| Publisher | : |
| Total Pages | : 340 |
| Release | : 1970 |
| Genre | : Mathematics |
| ISBN | : |
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