Petr Kulish's Books

Noncommutative Spacetimes

Symmetries in Noncommutative Geometry and Field Theory

By: Paolo Aschieri,Marija Dimitrijevic,Petr Kulish,Fedele Lizzi,Julius Wess

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Noncommutative Spacetimes

Symmetries in Noncommutative Geometry and Field Theory

By: Paolo Aschieri,Marija Dimitrijevic,Petr Kulish,Fedele Lizzi,Julius Wess

There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

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Page Count

205

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Springer

Published Date

ISBN 10

3540897933

ISBN 13

9783540897934

Infinite Dimensional Algebras and Quantum Integrable Systems

By: Petr P. Kulish

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Infinite Dimensional Algebras and Quantum Integrable Systems

By: Petr P. Kulish

This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics. Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields. Contributors: E. Frenkel O.A. Castro-Alvaredo and A. Fring V.G. Kac and M. Wakimoto A. Gerasimov, S. Kharchev and D. Lebedev H.E. Boos, V.E. Korepin and F.A. Smirnov Kanehisa Takasaki Takashi Takebe L.A. Takhtajan and Lee-Peng Teo V. Tarasov

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278

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Springer Science & Business Media

Published Date

ISBN 10

376437215X

ISBN 13

9783764372156

Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects

By: Massimo Blasone,Petr Jizba,Giuseppe Vitiello

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Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects

By: Massimo Blasone,Petr Jizba,Giuseppe Vitiello

Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets and crystals. Even large scale structures in the Universe and ordering in biological systems appear to be the manifestation of microscopic dynamics ruling their elementary components. The scope of this book is to answer questions such as: how it happens that the mesoscopic/macroscopic scale and stability characterizing those systems are dynamically generated out of the microscopic scale of fluctuating quantum components; how quantum particles coexist and interact with classically behaving macroscopic objects, e.g. vortices, magnetic domains and other topological defects. The quantum origin of topological defects and their interaction with quanta is a crucial issue for the understanding of symmetry breaking phase transitions and structure formation in a wide range of systems from condensed matter to cosmology. Deliberately not discussing other important problems, primarily renormalization problems, this book provides answers to such questions in a unitary, self-consistent physical and mathematical framework, which makes it unique in the panorama of existing texts on a similar subject. Crystals, ferromagnets and superconductors appear to be macroscopic quantum systems, i.e. their macroscopic properties cannot be explained without recourse to the underlying quantum dynamics. Recognizing that quantum field dynamics is not confined to the microscopic world is one of the achievements of this book, also marking its difference from other texts. The combined use of algebraic methods, and operator and functional formalism constitutes another distinctive, valuable feature./a

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Page Count

545

Publisher

World Scientific

Published Date

ISBN 10

1908978686

ISBN 13

9781908978684

Noncommutative Spacetimes

Symmetries in Noncommutative Geometry and Field Theory

By: Paolo Aschieri,Marija Dimitrijevic,Petr Kulish,Fedele Lizzi,Julius Wess

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Noncommutative Spacetimes

Symmetries in Noncommutative Geometry and Field Theory

By: Paolo Aschieri,Marija Dimitrijevic,Petr Kulish,Fedele Lizzi,Julius Wess

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Page Count

199

Publisher

Springer

Published Date

ISBN 10

3540897941

ISBN 13

9783540897941

Infinite Dimensional Algebras and Quantum Integrable Systems

By: Petr P. Kulish,Nenad Manojlovic,Henning Samtleben

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Infinite Dimensional Algebras and Quantum Integrable Systems

By: Petr P. Kulish,Nenad Manojlovic,Henning Samtleben

This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.

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266

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Springer Science & Business Media

Published Date

ISBN 10

3764373415

ISBN 13

9783764373412

Quantum Groups

Proceedings of Workshops held in the Euler International Mathematical Institute, Leningrad, Fall 1990

By: Petr P. Kulish

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Quantum Groups

Proceedings of Workshops held in the Euler International Mathematical Institute, Leningrad, Fall 1990

By: Petr P. Kulish

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.

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Page Count

408

Publisher

Springer

Published Date

ISBN 10

3662171511

ISBN 13

9783662171516

Book's by Petr Kulish

Noncommutative Spacetimes

Noncommutative Spacetimes

Infinite Dimensional Algebras and Quantum Integrable Systems

Infinite Dimensional Algebras and Quantum Integrable Systems

Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects

Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects

Noncommutative Spacetimes

Noncommutative Spacetimes

Infinite Dimensional Algebras and Quantum Integrable Systems

Infinite Dimensional Algebras and Quantum Integrable Systems

Quantum Groups

Quantum Groups

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