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This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.

Owing to efforts in both theoretical and experimental research, a better understanding of the interpretation and many fundamental principles of quantum mechanics has been achieved. These include the complementarity principle, the geometrical phase, the topological phase, the boundary between quantum and classical mechanics, quantum mechanics on the macroscopic level, and so on. Part of this book is devoted to introducing these developments.Significant progress in the frontier research in various branches of physics has been achieved by making use of the insights and judgements originating from quantum mechanics. Part of this book is devoted to introducing some of these fields, namely quantum information, cavity quantum electrodynamics, the quantum Hall effect and the Bose–Einstein condensation. Basic physical ideas and methods are emphasized, instead of going into technical details.The Yang–Baxter system has become a prosperous field of mathematical physics. The last part of the book is devoted to introducing its application to some basic problems in quantum mechanics, and again basic physical ideas are emphasized.

Both a theoretical physicist and mathematician, Ludwig Faddeev is best known for "the Faddeev equations", the first mathematically well-posed formulation of the quantum-mechanical three-body problem, which are foundational in few-body physics. Having made multiple seminal contributions to theoretical physics (Faddeev–Popov ghosts, Faddeev–Senjanovic quantization, Faddeev–Jackiw quantization among others), he was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize, the Dirac Prize, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others.A gathering of contributions from some of the biggest names in physics and mathematics, this volume serves as a tribute to this legendary figure in mathematical physics. Volume contributors include: Fields medallist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Louis Nirenberg, Samson Shatashvili, Vladimir Korepin as well as Nobel laureates Frank Wilczek, C N Yang and Gerard 't Hooft.

This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.

This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime.All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects.

'Professor Hao Bailin is one of China's most talented and most versatile theoretical physicists. He has made important contributions to a wide variety of research fields, including biology in which he pioneered a multidimensional method for studying the evolutionary pathways of bacteria. Indeed he calls himself, appreciatively I believe, a guerrilla fighter.'Nobel Laureate, Chen-Ning Yang