Proceedings Of The Second International Symposium On Quantum Theory And Symmetries

This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .

This volume gives a representative survey of recent developments in relativistic and non-relativistic quantum theory, which are related to the application of symmetries in their most general sense. The corresponding mathematical notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. Special emphasis is on results in the following areas: quantization methods, nonlinear evolution equations, foundation of quantum physics, algebraic quantum field theory, gauge and string theories, quantum information, quantum groups, discrete symmetries.

The book contains the text of lectures given at the third of a series of biennial symposia in mathematical physics held in odd-numbered years. The subject of the symposium is the frontiers of mathematical physics. It deals with quantum phenomena and includes topics such as string theory and quantum gravity, particle physics and field theory, non-communative geometry, integrable models and infinite dimensional symmetry groups, quantum computing and information processing, and quantum chaos. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Freydoon Mansouri Memorial LecturesAlgebras and RepresentationsQuantization and Quantum GravityD<4 Field TheoriesString and Brane WorldvolumesD>3 Field Theories and GravityString TheoryLoop Quantum GravityLorentz ViolationApplications Readership: Researchers, academics and postgraduates in high energy physics, mathematical physics and atomic physics. Keywords:Mathematical Physics;Strings;Quantum Gravity;Noncommutative Geometry

This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry. Contents:The Interacting Fock Space of Haldane's Exclusion Statistics (L Accardi & M Nhani)Complex Hamiltonians Having Real Spectra (C M Bender)From Rsonances to Poincaré Semigroups (A R Bohm et al.)Quantum Field Theory as Dynamical System (H J Borchers)Beta-lattices for Aperiodic Order (J-P Gazeau)Generalized Symmetries and Time (M Heller)Integrable Hierarchies and the WDVV-equations (G F Helminck)Global Gauss Law for Lattice QCD (J Kijowski & G Rudolph)Quantum Entanglement and Symmetries (M Kus)From Noncommutative Space-time to Quantum Relativistic Symmetries with Fundamental Mass Parameter (J Lukierski)Tomographic Map within the Framework of Star-product Quantization (O V Man'ko et al.)Algorithmic Cooling and Scalable Quantum Computers: Ways to Improve the Space-time Requirements of the Algorithm (T Mor & Y Weinstein)Quantum Theory on the Torus with Magnetic Field (H Narnhofer)Nonlocal Reflection by Photonic Barriers (G Nimtz & A Haibel)Lightfront Formalism versus Holography & Chiral Scanning (B Schroer)Broken Symmetries (W Thirring)Guage Theories on Non-communtative Spaces (J Wess) Readership: Researchers, lecturers and graduate students in theoretical, mathematical and quantum physics. Keywords:

This volume gives an overview of the recent representative developments in relativistic and non-relativistic quantum theory, which are related to the application of various mathematical notions of various symmetries. These notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. The emphasis is on results in the following areas: foundation of quantum physics, quantization methods, nonlinear quantum mechanics, algebraic quantum field theory, gauge and string theories, discrete spaces, quantum groups and generalized symmetries.

This book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.