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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, Jurg Froehlich, Roman Jackiw, Louis
Nirenberg, Samson Shatashvili, Vladimir Korepin as well as Nobel
laureates Frank Wilczek, C N Yang and Gerard 't Hooft.
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.
"The first volume might be especially useful for specialists in its
subject, but it also contains good expositions for nonspecialists."
Acta Sci. Math. (Szeged) Contents: Notes on Subfactors and
Statistical Mechanics (V F R Jones); Polynomial Invariants in Knot
Theory (L H Kauffman); Algebras of Loops on Surfaces, Algebras of
Knots, and Quantization (V G Turaev); Quantum Groups (L Faddeev et
al.); Introduction to the Yang-Baxter Equation (M Jimbo);
Integrable Systems Related to Braid Groups and Yang-Baxter Equation
(T Kohno); The Yang-Baxter Relation: A New Tool for Knot Theory (Y
Akutsu et al.); Akutsu-Wadati Link Polynomials from
Feynman-Kauffman Diagrams (M-L Ge et al.); Quantum Field Theory and
the Jones Polynomial (E Witten)
"The first volume might be especially useful for specialists in its
subject, but it also contains good expositions for nonspecialists."
Acta Sci. Math. (Szeged) Contents: Notes on Subfactors and
Statistical Mechanics (V F R Jones); Polynomial Invariants in Knot
Theory (L H Kauffman); Algebras of Loops on Surfaces, Algebras of
Knots, and Quantization (V G Turaev); Quantum Groups (L Faddeev et
al.); Introduction to the Yang-Baxter Equation (M Jimbo);
Integrable Systems Related to Braid Groups and Yang-Baxter Equation
(T Kohno); The Yang-Baxter Relation: A New Tool for Knot Theory (Y
Akutsu et al.); Akutsu-Wadati Link Polynomials from
Feynman-Kauffman Diagrams (M-L Ge et al.); Quantum Field Theory and
the Jones Polynomial (E Witten)
'The book is an engaging and influential collection of significant
contributions from an assembly of world expert leaders and pioneers
from different fields, working at the interface between topology
and physics or applications of topology to physical systems ... The
book explores many interesting and novel topics that lie at the
intersection between gravity, quantum fields, condensed matter,
physical cosmology and topology ... A rich, well-organized, and
comprehensive overview of remarkable and insightful connections
between physics and topology is here made available to the physics
reader.'Contemporary PhysicsSince its birth in Poincare's seminal
1894 'Analysis Situs', topology has become a cornerstone of
mathematics. As with all beautiful mathematical concepts, topology
inevitably - resonating with that Wignerian principle of the
effectiveness of mathematics in the natural sciences - finds its
prominent role in physics. From Chern-Simons theory to topological
quantum field theory, from knot invariants to Calabi-Yau
compactification in string theory, from spacetime topology in
cosmology to the recent Nobel Prize winning work on topological
insulators, the interactions between topology and physics have been
a triumph over the past few decades.In this eponymous volume, we
are honoured to have contributions from an assembly of grand
masters of the field, guiding us with their world-renowned
expertise on the subject of the interplay between 'Topology' and
'Physics'. Beginning with a preface by Chen Ning Yang on his
recollections of the early days, we proceed to a novel view of
nuclei from the perspective of complex geometry by Sir Michael
Atiyah and Nick Manton, followed by an entree toward recent
developments in two-dimensional gravity and intersection theory on
the moduli space of Riemann surfaces by Robbert Dijkgraaf and
Edward Witten; a study of Majorana fermions and relations to the
Braid group by Louis H Kauffman; a pioneering investigation on
arithmetic gauge theory by Minhyong Kim; an anecdote-enriched
review of singularity theorems in black-hole physics by Sir Roger
Penrose; an adventure beyond anyons by Zhenghan Wang; an apercu on
topological insulators from first-principle calculations by Haijun
Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum
information theory as one of the four revolutions in physics and
the second quantum revolution by Xiao-Gang Wen. We hope that this
book will serve to inspire the research community.
'The book is an engaging and influential collection of significant
contributions from an assembly of world expert leaders and pioneers
from different fields, working at the interface between topology
and physics or applications of topology to physical systems ... The
book explores many interesting and novel topics that lie at the
intersection between gravity, quantum fields, condensed matter,
physical cosmology and topology ... A rich, well-organized, and
comprehensive overview of remarkable and insightful connections
between physics and topology is here made available to the physics
reader.'Contemporary PhysicsSince its birth in Poincare's seminal
1894 'Analysis Situs', topology has become a cornerstone of
mathematics. As with all beautiful mathematical concepts, topology
inevitably - resonating with that Wignerian principle of the
effectiveness of mathematics in the natural sciences - finds its
prominent role in physics. From Chern-Simons theory to topological
quantum field theory, from knot invariants to Calabi-Yau
compactification in string theory, from spacetime topology in
cosmology to the recent Nobel Prize winning work on topological
insulators, the interactions between topology and physics have been
a triumph over the past few decades.In this eponymous volume, we
are honoured to have contributions from an assembly of grand
masters of the field, guiding us with their world-renowned
expertise on the subject of the interplay between 'Topology' and
'Physics'. Beginning with a preface by Chen Ning Yang on his
recollections of the early days, we proceed to a novel view of
nuclei from the perspective of complex geometry by Sir Michael
Atiyah and Nick Manton, followed by an entree toward recent
developments in two-dimensional gravity and intersection theory on
the moduli space of Riemann surfaces by Robbert Dijkgraaf and
Edward Witten; a study of Majorana fermions and relations to the
Braid group by Louis H Kauffman; a pioneering investigation on
arithmetic gauge theory by Minhyong Kim; an anecdote-enriched
review of singularity theorems in black-hole physics by Sir Roger
Penrose; an adventure beyond anyons by Zhenghan Wang; an apercu on
topological insulators from first-principle calculations by Haijun
Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum
information theory as one of the four revolutions in physics and
the second quantum revolution by Xiao-Gang Wen. We hope that this
book will serve to inspire the research community.
Yi-Shi Duan (1927-2016) was one of the world-renowned pioneers in
the study of gauge field theory and general relativity. Trained in
the former Soviet Union, Prof. Duan returned to China in 1957 to
work in Lanzhou University for 60 years. In 1963, he came up with a
general co-variant form of the conservation law of the
energy-momentum tensor in general relativity. In 1979, he suggested
that the gauge potential could be decomposed, which has important
implications to gauge field theory. He trained in China a big team
of talents in theoretical physics. His contributions to theoretical
physics in China have earned him praise from both Professor
Shiing-Shen Chern and Professor Chen-Ning Yang.
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 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.
'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.'Chen-Ning
Yang, Nobel Laureate
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.
This volume focuses on developments in the field of group theory in
its broadest sense and is of interest to theoretical and
experimental physicists, mathematicians, and scientists in related
disciplines who are interested in the latest methods and
applications. In an increasingly ultra-specialized world, this
volume will demonstrate the interchange of ideas and methods in
theoretical and mathematical physics.
The book aims to survey recent developments in quantum algebras and
related topics. Quantum groups were introduced by Drinfeld and
Jimbo in 1985 in their work on Yang Baxter equations. The subject
from the very beginning has been an interesting one for both
mathematics and theoretical physics. For example, Yangian is a
special example of quantum group, corresponding to rational
solution of Yang Baxter equation. Viewed as a generalization of the
symmetric group, Yangians also have close connections to algebraic
combinatorics. This is the proceeding for the International
Workshop on Quantized Algebra and Physics. The workshop aims to
gather experts and young investigators from China and abroad to
discuss research problems in integrable systems, conformal field
theory, string theory, Lie theory, quantum groups including
Yangians and their representations.
This volume contains the lectures given by the three speakers, M
Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in
their field. It is essential reading to those working in the fields
of Quantum Groups, and Integrable Systems.
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