Lie Groups Quantization Volume 2
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| Author | : Veronique Fischer |
| Publisher | : Birkhäuser |
| Total Pages | : 568 |
| Release | : 2016-03-08 |
| Genre | : Mathematics |
| ISBN | : 3319295586 |
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
| Author | : Peter Woit |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2017-11-01 |
| Genre | : Science |
| ISBN | : 3319646125 |
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.
| Author | : Roger William Carter |
| Publisher | : Cambridge University Press |
| Total Pages | : 662 |
| Release | : 2005-10-27 |
| Genre | : Mathematics |
| ISBN | : 9780521851381 |
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
| Author | : Francesco Iachello |
| Publisher | : Springer |
| Total Pages | : 208 |
| Release | : 2007-02-22 |
| Genre | : Science |
| ISBN | : 3540362398 |
This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
| Author | : Sean Bates |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 150 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780821807989 |
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
| Author | : Garth Warner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 501 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642516408 |
| Author | : Jørgen Ellegaard Andersen |
| Publisher | : Oxford University Press |
| Total Pages | : 400 |
| Release | : 2018-10-18 |
| Genre | : Mathematics |
| ISBN | : 019252237X |
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
| Author | : Victor G. Kac |
| Publisher | : Springer |
| Total Pages | : 545 |
| Release | : 2018-12-12 |
| Genre | : Mathematics |
| ISBN | : 3030021912 |
This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
| Author | : Heinrich G. W. Begehr |
| Publisher | : World Scientific |
| Total Pages | : 1557 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 981238572X |
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
| Author | : Josi A. de Azcárraga |
| Publisher | : Cambridge University Press |
| Total Pages | : 480 |
| Release | : 1998-08-06 |
| Genre | : Mathematics |
| ISBN | : 9780521597005 |
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
