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

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. .

In this major new study in the sociology of scientific knowledge, social theorist Mohammad H. Tamdgidi reports having unriddled the so-called ‘quantum enigma.’ This book opens the lid of the Schrödinger’s Cat box of the ‘quantum enigma’ after decades and finds something both odd and familiar: Not only the cat is both alive and dead, it has morphed into an elephant in the room in whose interpretation Einstein, Bohr, Bohm, and others were each both right and wrong because the enigma has acquired both localized and spread-out features whose unriddling requires both physics and sociology amid both transdisciplinary and transcultural contexts. The book offers, in a transdisciplinary and transcultural sociology of self-knowledge framework, a relativistic interpretation to advance a liberating quantum sociology. Deeper methodological grounding to further advance the sociological imagination requires investigating whether and how relativistic and quantum scientific revolutions can induce a liberating reinvention of sociology in favor of creative research and a just global society. This, however, necessarily leads us to confront an elephant in the room, the ‘quantum enigma.’ In Unriddling the Quantum Enigma, the first volume of the series commonly titled Liberating Sociology: From Newtonian toward Quantum Imaginations, sociologist Mohammad H. Tamdgidi argues that unriddling the ‘quantum enigma’ depends on whether and how we succeed in dehabituating ourselves in favor of unified relativistic and quantum visions from the historically and ideologically inherited, classical Newtonian modes of imagining reality that have subconsciously persisted in the ways we have gone about posing and interpreting (or not) the enigma itself for more than a century. Once this veil is lifted and the enigma unriddled, he argues, it becomes possible to reinterpret the relativistic and quantum ways of imagining reality (including social reality) in terms of a unified, nonreductive, creative dialectic of part and whole that fosters quantum sociological imaginations, methods, theories, and practices favoring liberating and just social outcomes. The essays in this volume develop a set of relativistic interpretive solutions to the quantum enigma. Following a survey of relevant studies, and an introduction to the transdisciplinary and transcultural sociology of self-knowledge framing the study, overviews of Newtonianism, relativity and quantum scientific revolutions, the quantum enigma, and its main interpretations to date are offered. They are followed by a study of the notion of the “wave-particle duality of light” and the various experiments associated with the quantum enigma in order to arrive at a relativistic interpretation of the enigma, one that is shown to be capable of critically cohering other offered interpretations. The book concludes with a heuristic presentation of the ontology, epistemology, and methodology of what Tamdgidi calls the creative dialectics of reality. The volume essays involve critical, comparative/integrative reflections on the relevant works of founding and contemporary scientists and scholars in the field. This study is the first in the monograph series “Tayyebeh Series in East-West Research and Translation” of Human Architecture: Journal of the Sociology of Self-Knowledge (XIII, 2020), published by OKCIR: Omar Khayyam Center for Integrative Research in Utopia, Mysticism, and Science (Utopystics). OKCIR is dedicated to exploring, in a simultaneously world-historical and self-reflective framework, the human search for a just global society. It aims to develop new conceptual (methodological, theoretical, historical), practical, pedagogical, inspirational and disseminative structures of knowledge whereby the individual can radically understand and determine how world-history and her/his selves constitute one another. Reviews “Mohammad H. Tamdgidi’s Liberating Sociology: From Newtonian Toward Quantum Imaginations, Volume 1, Unriddling the Quantum Enigma hits the proverbial nail on the head of an ongoing problem not only in sociology but also much social science—namely, many practitioners’ allegiance, consciously or otherwise, to persisting conceptions of ‘science’ that get in the way of scientific and other forms of theoretical advancement. Newtonianism has achieved the status of an idol and its methodology a fetish, the consequence of which is an ongoing failure to think through important problems of uncertainty, indeterminacy, multivariation, multidisciplinarity, and false dilemmas of individual agency versus structure, among many others. Tamdgidi has done great service to social thought by bringing to the fore this problem of disciplinary decadence and offering, in effect, a call for its teleological suspension—thinking beyond disciplinarity—through drawing upon and communicating with the resources of quantum theory not as a fetish but instead as an opening for other possibilities of social, including human, understanding. The implications are far-reaching as they offer, as the main title attests, liberating sociology from persistent epistemic shackles and thus many disciplines and fields connected to things ‘social.’ This is exciting work. A triumph! The reader is left with enthusiasm for the second volume and theorists of many kinds with proverbial work to be done.” — Professor Lewis R. Gordon, Honorary President of the Global Center for Advanced Studies and author of Disciplinary Decadence: Living Thought in Trying Times (Routledge/Paradigm, 2006), and Freedom, Justice, and Decolonization (Routledge, forthcoming 2020) "Social sciences are still using metatheoretical models of science based on 19th century newtonian concepts of "time and space". Mohammad H. Tamdgidi has produced a 'tour de force' in social theory leaving behind the old newtonian worldview that still informs the social sciences towards a 21st century non-dualistic, non-reductionist, transcultural, transdisciplinary, post-Einsteinian quantum concept of TimeSpace. Tamdgidi goes beyond previous efforts done by titans of social theory such as Immanuel Wallerstein and Kyriakos Kontopoulos. This book is a quantum leap in the social sciences at large. Tamdgidi decolonizes the social sciences away from its Eurocentric colonial foundations bringing it closer not only to contemporary natural sciences but also to its convergence with the old Eastern philosophical and mystical worldviews. This book is a masterpiece in social theory for a 21st century decolonial social science. A must read!" — Professor Ramon Grosfoguel, University of California at Berkeley​​​​​​​ "Tamdgidi’s Liberating Sociology succeeds in adding physical structures to the breadth of the world-changing vision of C. Wright Mills, the man who mentored me at Columbia. Relativity theory and quantum mechanics can help us to understand the human universe no less than the physical universe. Just as my Creating Life Before Death challenges bureaucracy’s conformist orientation, so does Liberating Sociology“liberate the infinite possibilities inherent in us.” Given our isolation in the Coronavirus era, we have time to follow Tamdgidi in his journey into the depth of inner space, where few men have gone before. It is there that we can gain emotional strength, just as Churchill, Roosevelt and Mandela empowered themselves. That personal development was needed to address not only their own personal problems, but also the mammoth problems of their societies. We must learn to do the same." — Bernard Phillips, Emeritus Sociology Professor, Boston University

This volume is a collection of lectures given by distinguished physicists from around the world, covering the most recent advances in theoretical physics and the latest results from current experimental facilities.Following one of the principal aims of the School ? to encourage and promote young physicists to achieve recognition at an international level ? the students who distinguished themselves for the excellence of their research were given the opportunity to publish their presentations in this volume.

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: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."