Quantum theory, groups and representations, Woit, Peter
Автор: Anatoli Klimyk; Konrad Schm?dgen Название: Quantum Groups and Their Representations ISBN: 3642646018 ISBN-13(EAN): 9783642646010 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The invention of quantum groups is one of the outstanding achievements of mathematical physics and mathematics in the late twentieth century. The birth of the new theory and its rapid development are results of a strong interrelation between mathematics and physics. Quantu groups arose in the work of L.D. Faddeev and the Leningrad school on the inverse scattering method in order to solve integrable models. The algebra Uq(sh) appeared first in 1981 in a paper by P.P. Kulish and N.Yu. Reshetikhin on the study of integrable XYZ models with highest spin. Its Hopf algebra structure was discovered later by E.K. Sklyanin. A major event was the discovery by V.G. Drinfeld and M. Jimbo around 1985 of a class of Hopf algebras which can be considered as one-parameter deforma- tions of universal enveloping algebras of semisimple complex Lie algebras. These Hopf algebras will be called Drinfeld-Jimbo algebras in this book. Al- most simultaneously, S.L. Woronowicz invented the quantum group SUq(2) and developed his theory of compact quantum matrix groups. An algebraic approach to quantized coordinate algebras was given about this time by Yu.I. Manin.
Автор: Hermann Weyl. Название: The Classical Groups: Their Invariants and Representations ISBN: 0691057567 ISBN-13(EAN): 9780691057569 Издательство: Wiley Рейтинг: Цена: 14573.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discusses the symmetric, linear, orthogonal, and symplectic groups and determines their invariants and representations. This book covers topics such as matrix algebras, semigroups, commutators, and spinors, which help in understanding the group-theoretic structure of quantum mechanics.
Автор: Philipp Niemann; Robert Wille Название: Compact Representations for the Design of Quantum Logic ISBN: 3319637231 ISBN-13(EAN): 9783319637235 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality.
Описание: Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory.
Описание: This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jorgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.
Автор: Vvedensky Dimitri D, Evans Timothy S Название: Symmetry, Groups, And Representations In Physics ISBN: 1786340151 ISBN-13(EAN): 9781786340153 Издательство: World Scientific Publishing Цена: 10138.00 р. Наличие на складе: Поставка под заказ.
Описание: This book is an introduction to symmetry in physics based on discrete and continuous groups. No knowledge of algebra is assumed and the book is suitable for both beginning and advanced graduate students. In fact, at Imperial College, the notes on which this book is based have been thoroughly tested in the classroom by two lecturers with quite different backgrounds (condensed matter theory and field theory) to classes composed of third- and fourth-year undergraduate students as well as students from the MSc in Quantum Fields and Fundamental Forces program. Abundant exercises, all with detailed solutions that are available in a separate instructor's manual, are included to illustrate the concepts introduced in the main text, to extend some of the main results, and to introduce new ideas. One of the main themes in the book is the application of group theory to physical problems.
Описание: 'All are every interesting topics treated with a high level of mathematical sophistication. One of the very useful tricks the author repeatedly resorts to is the introduction of one-parameter families of operators interpolating between two operators which appear naturally in the formalism. From this one-parameter family a differential equation for the determinant (or ratio of determinants) or for correlation functions is derived, which can then be solved. This is a very simple, elegant and powerful technique.'Mathematical Reviews ClippingsFunctional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.
Описание: At the time I learned quantum field theory it was considered a folk theo- rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of a theory fulfilling locality without a pos- itive energy representation was first done by Doplicher, Regge, and Singer [DRS].
Описание: Aimed at advanced students and active researchers in mathematics or theoretical physics, this book provides a detailed exposition of automorphic forms and representations, from the basics up to cutting-edge research topics at the interface between number theory and string theory.
Описание: Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory.
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