This book provides a comprehensive collection of problems together with their detailed solutions for Bose, Spin, Fermi systems and also interacting systems. Supplementary problems are also provided. Exercises for representations of Lie groups and Lie algebras are also covered as well as computer algebra implementations. It is the only book which summarizes these topics from the quantum theory aspect in the form of exercises and solutions. The book is also self-contained.Both physicists and mathematicians will benefit from all the different techniques explained and worked out in detail.
This book provides a comprehensive collection of problems together with their detailed solutions for Bose, Spin, Fermi systems and also interacting systems. Supplementary problems are also provided. Exercises for representations of Lie groups and Lie algebras are also covered as well as computer algebra implementations. It is the only book which summarizes these topics from the quantum theory aspect in the form of exercises and solutions. The book is also self-contained. Both physicists and mathematicians will benefit from all the different techniques explained and worked out in detail.
The application of field theoretic techniques to problems in condensed matter physics has generated an array of concepts and mathematical techniques to attack a range of problems such as the theory of quantum phase transitions, the quantum Hall effect, and quantum wires. While concepts such as the renormalization group, topology, and bosonization h
The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.
'This is an excellent, well-written and very comprehensive book covering many topics of mathematics and physics. An exhaustive collection of problems with detailed solutions that may be valuable to students and young researchers in several fields, ranging from Mathematics to Quantum Physics is presented … I found the book helpful in regards to several subjects that are not covered in other mathematical physics introductory textbooks.'Contemporary PhysicsThis updated and extended edition of the book combines the topics provided in the two parts of the previous editions as well as new topics. It is a comprehensive compilation covering most areas in mathematical and theoretical physics. The book provides a collection of problems together with their detailed solutions which will prove to be valuable to students as well as to researchers in the fields of mathematics, physics, engineering and other sciences.Each chapter provides a short introduction with the relevant definitions and notations. All relevant definitions are given. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Stimulating supplementary problems are also provided in each chapter. Students can learn important principles and strategies required for problem solving. Teachers will also find this text useful as a supplement, since important concepts and techniques are developed in the problems. Introductory problems for both undergraduate and advanced undergraduate students are provided. More advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover new fields in theoretical and mathematical physics such as tensor product, Lax representation, Bäcklund transformation, soliton equations, Hilbert space theory, uncertainty relation, entanglement, spin systems, Lie groups, Bose system, Fermi systems differential forms, Lie algebra valued differential forms, metric tensor fields, Hirota technique, Painlevé test, Bethe ansatz, Yang-Baxter relation, wavelets, gauge theory, differential geometry, string theory, chaos, fractals, complexity, ergodic theory, etc. A number of software implementations are also provided.
This book provides a comprehensive collection of problems together with their detailed solutions in the field of Theoretical and Mathematical Physics. All modern fields in Theoretical and Mathematical Physics are covered. It is the only book which covers all the new techniques and methods in theoretical and mathematical physics.Third edition updated with: Exercises in: Hilbert space theory, Lie groups, Matrix-valued differential forms, Bose-Fermi operators and string theory. All other chapters have been updated with new problems and materials. Most chapters contain an introduction to the subject discussed in the text.
This book explores the physics of atoms frozen to ultralow temperatures and trapped in periodic light structures. It introduces the reader to the spectacular progress achieved on the field of ultracold gases and describes present and future challenges in condensed matter physics, high energy physics, and quantum computation.
Contents:Nonlinear Problems in 1 + 1 and Their LinearizationClassical Field Theory ModelsHamiltonian Formulation, Action-Angle Variables, Solitons, Classical Lattice Models and Lattice Approximants of Classical FieldsQuantization on a Lattice: Relationship Classical-QuantumQuantization on a Lattice: Simple Bose ModelsSpin 1/2 Lattice Systems Related to Nonlinear Bose Problems: Lattice FermionsQuantization in Continuum: Joint Bose-Fermi Spectral Problems in 1 + 1Quantum Meaning of Classical Field Theory for Fermi SystemsOn Infinite Constituent “Elementary” Systems: Canonical (Constituent) Quantization of Soliton FieldsTowards 1 + 3: Problems and Prospects Readership: Mathematical physicists and physicists. Keywords:Nonlinear Fields;Integrability;Solvable Models;Solitons;Continuum and Lattice Models;Quantization;Fermi Fields And Their Classical Counterparts;Relationship Classical-Quantum;Boson-Fermion Reciprocity (Bosonization)
