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Tuesday, July 14, 2020 | History

1 edition of Quantum groups and quantum spaces found in the catalog.

Quantum groups and quantum spaces

Quantum groups and quantum spaces

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  • 30 Currently reading

Published by Polish Academy of Sciences, Institute of Mathematics in Warszawa .
Written in English

    Subjects:
  • Quantum groups -- Congresses.,
  • Locally compact groups -- Congresses.,
  • Lie algebras -- Congresses.,
  • Lie groups -- Congresses.,
  • Differential calculus -- Congresses.,
  • Hopf algebras -- Congresses.

  • Edition Notes

    Statementeditors of the volume, Robert Budzyński, Wiesław Pusz, Stanisław Zakrzewski.
    SeriesBanach Center publications,, v. 40
    ContributionsBudzyński, Robert., Pusz, Wiesław., Zakrzewski, Stanisław, 1951-1998.
    Classifications
    LC ClassificationsQC20.7.G76 Q83 1997
    The Physical Object
    Pagination441 p. :
    Number of Pages441
    ID Numbers
    Open LibraryOL296349M
    LC Control Number97202533
    OCLC/WorldCa37396931

    1 day ago  The quantum distance measures the quantum mechanical distance between two Bloch wave functions. (Right) Bloch wave functions of the flat band can be represented by the pseudo-spin (arrows). The Keith Group's research compilation, "Computational Quantum Chemical Explorations of Chemical/Material Space for Efficient Electrocatalysts," was .

    Lectures on Quantum Groups by Pavel Etingof and Olivier Schiffmann International Press Get this from a library! Quantum groups and noncommutative spaces: perspectives on quantum geometry: a publication of the Max-Planck-Institute for Mathematics, Bonn. [Matilde Marcolli; D Parashar;].

    A Preview of Quantum Physics 15 Quantum Physics and Computation 19 2 LINEAR ALGEBRA AND THE DIRAC NOTATION 21 The Dirac Notation and Hilbert Spaces 21 Dual Vectors 23 Operators 27 The Spectral Theorem 30 Functions of Operators 32 Tensor Products 33 The Schmidt Decomposition Theorem   Both theories are, according to Jim Baggott, “extraordinarily successful”. The problem, as he outlines in the preface to ‘Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time and the Universe’ (Oxford University Press, £20, ISBN ), is that they are mutually incompatible.


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Quantum groups and quantum spaces Download PDF EPUB FB2

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo inor variations thereof.

The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties.

Quantum groups and quantum spaces. Warszawa: Polish Academy of Sciences, Institute of Mathematics, (OCoLC) Material Type: Conference publication: Document Type: Book: All Authors / Contributors: Robert Budzyński; Wiesław Pusz; Stanisław Zakrzewski.

This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches.

It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra.

The geometry of a compact matrix quantum group is a special case of a noncommutative geometry. The continuous complex-valued functions on a compact Hausdorff topological space form a commutative C.

Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] (∗-) algebra theory, theory of compact (matrix) quantum groups and the theory of their actions on compact quantum spaces.

We also provide the most important examples, in-cluding the classification of quantum SL(2)-groups, their real forms and quantum spheres. We also consider quantum SLq(N)-groups and quantum Lorentz groups. Contents 1.

This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the.

This textbook presents an expanded write-up of Manin's celebrated Montreal author systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others.

Quantum vector spaces were basically invented by Manin in his book, ``Noncommutative Geometry and Quantum Groups,'' and I will only be talking about a subclass of his quantum vector spaces. To get at the concept, you have to think like an algebraic geometer -- or a quantum field theorist.

This book is devoted to the consistent and systematic application of group theory to quantum mechanics. Beginning with a detailed introduction to the classical theory of groups, Dr. Weyl continues with an account of the fundamental results of quantum physics. Search within book. Front Matter. Pages i-xii.

PDF. Quantum SL(2) Front Matter. Pages PDF. Preliminaries. Christian Kassel. Quantum Groups and Monodromy. Front Matter. Pages PDF. Generalities on Quantum Enveloping Algebras. Group representation Lie algebra Vector space algebra cohomology topology.

Authors and affiliations. pact quantum groups (see Section 5 below). Thus if there is any natural topology on EA(G), the relation with continuous fields of ergodic ac-tions should be clarified.

One distinct feature of the theory of compact quantum groups is that there is a full compact quantum group and a reduced compact group. 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.

Quantum Computation and Quantum Information is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject.

It is informally known as "Mike and Ike", after the candies of that book assumes minimal prior experience with quantum mechanics and with computer science, aiming instead.

The best book I can think of for this subject at the moment is The Quantum Theory of Fields, Volume 1: Foundations.

I am not recommending you to read quantum field theory. This book contains the best introduction of quantum mechanics in chapter 1 and chapter 2, using rigorous group representation theory in Hilbert space, but is very readable for physicists.

Quantum Space (Quantum Series Book 1) - Kindle edition by Phillips, Douglas. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Quantum Space (Quantum Series Book 1).Reviews: K.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita (ed.). Publisher: MDPI AG ISBN Number of pages: Description: Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are.

"Quantum Space" and "Quantum Void" are Star books but most of "Quantum Time" feels like it was written by a completely different author. I read hard science fiction to avoid the inane, simple-minded genderizations and polarizations of our ridiculous culture but this book wallows in s: However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques.

A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. The thing that stands out in this book is its focus on real science.

Quantum Space puts the science in science fiction. (marketing, ha!) A lot of Quantum Space is pretty typical for a sci-fi book. It's characters are pretty flat. Human interaction, meh. That isn't the emphasis here.

The plot and the writing are okay/5(). The book you might consult on the subject is a classic one, by H Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications,ISBN A continuous (Lie) group SO(3) ~ SU(2) is generated by three generators, and its group elements are exponentials of all linear combinations of said generators.The algebraic study of quantum logics that generalize Boolean σ-algebras has given rise to the theory of orthomodular posets, and the study of states to non-commutative measure theory.

One of the most important quantum logic is the projection lattice of a Hilbert space H.The notion of a “quantum group” was introduced by V.G. Dinfel&dacute; and M.

Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras.