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After several decades of reduced contact, the interaction between
physicists and mathematicians in the front-line research of both
fields recently became deep and fruit ful again. Many of the
leading specialists of both fields became involved in this devel
opment. This process even led to the discovery of previously
unsuspected connections between various subfields of physics and
mathematics. In mathematics this concerns in particular knots von
Neumann algebras, Kac-Moody algebras, integrable non-linear partial
differential equations, and differential geometry in low
dimensions, most im portantly in three and four dimensional spaces.
In physics it concerns gravity, string theory, integrable classical
and quantum field theories, solitons and the statistical me chanics
of surfaces. New discoveries in these fields are made at a rapid
pace. This conference brought together active researchers in these
areas, reporting their results and discussing with other
participants to further develop thoughts in future new directions.
The conference was attended by SO participants from 15 nations.
These proceedings document the program and the talks at the
conference. This conference was preceded by a two-week summer
school. Ten lecturers gave extended lectures on related topics. The
proceedings of the school will also be published in the NATO-AS[
volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to
thank the many people who have made the conference a success.
Furthermore, *we appreciate the excellent talks. The active
participation of everyone present made the conference lively and
stimulating. All of this made our efforts worth while.
The 50-year history of weak interaction since Fermi's pro posal of
this coupling has been marked with striking direct inter plays
between experimental results and theoretical understanding, e.g.
the discoveries of neutrinos, parity violation, and CP vio lation.
The recent discoveries of the quark hierarchy, the charm and the
beauty, and the intermediate vector bosons W+/- and ZO have truly
made a splendid page in the history of particle physics. It is the
purpose of this conference to discuss the questions of quark and
lepton generations and mixing, their relations to CP violation, and
to ask the questions about what are inside the quarks and the
leptons in view of the present and future exper imental situation.
Dr. Ling-Lie Chau Brookhaven National Laboratory Upton, New York
vii ACKNOWLEDGMENTS I would like to thank all the Advisory and
Organizing Committee members for their advice and suggestions
during the organization of the conference. The running of the
conference could not have gone so smoothly without the help of many
participants, I sincerely thank: L. Becker, F.J. Botella, S.
Gentile, P. Le Comte, M.E. Machacek, L. Lanceri, W.M. Morse, F.J.
Olness, Y.-X. Pham, G. Poulard, K.J. Sliwa, and J.N. Webb.
Stanley Mandelstam (1928-2016) was one of the most influential and
respected particle theorists. Coming as a young chemical engineer
from South Africa to study theoretical physics in England, he
quickly became a leading physicist in his field. With his deep
understanding of quantum field theory, he pioneered the development
of the analytic S-matrix theory as well as the path-dependent
formulations for quantum gauge theories and for quantum general
relativity. They are being actively used for the electroweak theory
and having their imprints in lattice gauge theory and loop quantum
gravity. Also he elucidated the mechanisms for quark confinement in
quantum chromodynamics, constructed non-perturbative bosonization
methods in 1+1 dimensions, and proved the perturbative finiteness
and =0 of N=4 supersymmetric Yang-Mills theory. His work also led
to the discovery of dual resonance models, which in turn became
superstring theory. He was a leader in these developments, devoting
much of his later years to the proof that the theory is
perturbatively finite so it can be considered as a contender for
the theory of quantum gravity.He was also a very modest and
friendly man, impressing everyone with his sharp intellect as well
as his humanity. This volume contains essays written by many of his
friends and students, including both detailed reports on his
scientific achievements as well as personal reminiscences. Also
collected in the volume are some selected reprints of Mandelstam's
early seminal papers and abstracts of selected papers representing
the full spectrum of his contributions.
Stanley Mandelstam (1928-2016) was one of the most influential and
respected particle theorists. Coming as a young chemical engineer
from South Africa to study theoretical physics in England, he
quickly became a leading physicist in his field. With his deep
understanding of quantum field theory, he pioneered the development
of the analytic S-matrix theory as well as the path-dependent
formulations for quantum gauge theories and for quantum general
relativity. They are being actively used for the electroweak theory
and having their imprints in lattice gauge theory and loop quantum
gravity. Also he elucidated the mechanisms for quark confinement in
quantum chromodynamics, constructed non-perturbative bosonization
methods in 1+1 dimensions, and proved the perturbative finiteness
and =0 of N=4 supersymmetric Yang-Mills theory. His work also led
to the discovery of dual resonance models, which in turn became
superstring theory. He was a leader in these developments, devoting
much of his later years to the proof that the theory is
perturbatively finite so it can be considered as a contender for
the theory of quantum gravity.He was also a very modest and
friendly man, impressing everyone with his sharp intellect as well
as his humanity. This volume contains essays written by many of his
friends and students, including both detailed reports on his
scientific achievements as well as personal reminiscences. Also
collected in the volume are some selected reprints of Mandelstam's
early seminal papers and abstracts of selected papers representing
the full spectrum of his contributions.
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