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Geometric Methods in Physics
The Białowieża Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Białowieża natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100 participants from both the mathematics and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work was supplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, and on this occasion the discussion mainly focused on his contributions to mathematical physics such as deformation quantization, Poisson geometry, symplectic geometry and non-commutative differential geometry.
Geometric Methods in Physics XXXVII
The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Białowieża Workshops have been complemented by a School on Geometry and Physics comprising a series of advanced lectures for graduate students and early-career researchers. The book also includes abstracts of the five lecture series that were given at the seventh school.
Hopf Algebras in Noncommutative Geometry and Physics
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Reflections on Quanta, Symmetries, and Supersymmetries
This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.
Deformation Quantization
This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001. Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.
Physics and Necessity
Can we prove the necessity of our best physical theories by rational means, without appeal to experience? This book recounts a few ingenious attempts to derive physical theories by reason only, beginning with Descartes' geometric construction of the world, and finishing with recent derivations of quantum mechanics from natural axioms. Deductions based on theological, metaphysical, or transcendental arguments are worth remembering for the ways they motivated and structured physical theory, even though we would now criticize their excessive confidence in the power of the mind. Other deductions more modestly relied on criteria for the comprehensibility of nature, including forms of measurabilit...
Proceedings Of The Julian Schwinger Centennial Conference
The Julian Schwinger Centennial Conference of 2018 assembled many of Schwinger's students, colleagues, and friends to celebrate this towering figure of twentieth century physics one hundred years after his birth. This proceedings volume collects talks delivered on this occasion. They cover a wide range of topics, all related to Schwinger's rich scientific legacy — supplemented by personal recollections about Julian Schwinger, the physicist, the teacher, and the gentleman.Also included are an essay of 1985, co-authored by Schwinger but not published previously, as well as the transcripts of speeches by distinguished colleagues at the 1978 gathering when Schwinger's sixtieth birthday was celebrated.
Non-commutative Geometry in Mathematics and Physics
This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics.It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference.This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
Fantasies of Ito Michio
Born in Japan and trained in Germany, dancer and choreographer Ito Michio (1893–1961) achieved prominence in London before moving to the U.S. in 1916 and building a career as an internationally acclaimed artist. During World War II, Ito was interned for two years, and then repatriated to Japan, where he contributed to imperial war efforts by creating propaganda performances and performing revues for the occupying Allied Forces in Tokyo. Throughout, Ito continually invented stories of voyages made, artists befriended, performances seen, and political activities carried out—stories later dismissed as false. Fantasies of Ito Michio argues that these invented stories, unrealized projects, an...
Operators and Representation Theory
Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.
