|
Showing 1 - 3 of
3 matches in All Departments
Aconferenceon"NoncommutativeGeometryandtheStandardModelof-
ementaryParticlePhysics"washeldattheHesselbergAcademy(innorthern
Bavaria, Germany) during the week of March 14-19, 1999. The aim of
the conference was to give a systematic exposition of the
mathematical foun- tions and physical applications of
noncommutative geometry, along the lines developedbyAlainConnes.
Theconferencewasactuallypartofacontinuing series of conferences at
the Hesselberg Academy held every three years and devoted to
important developments in mathematical ?elds, such as geom-
ricanalysis, operatoralgebras, indextheory,
andrelatedtopicstogetherwith their applications to mathematical
physics. The participants of the conference included mathematicians
from fu- tional analysis, di?erential geometry and operator
algebras, as well as - perts from mathematical physics interested
in A. Connes' approach towards the standard model and other
physical applications. Thus a large range of topics, from
mathematical foundations to recent physical applications, could
becoveredinasubstantialway. Theproceedingsofthisconference,
organized in a coherent and systematic way, are presented here. Its
three chapters c- respond to the main areas discussed during the
conference: Chapter1. Foundations of Noncommutative Geometry and
Basic Model Building Chapter2. The Lagrangian of the Standard Model
Derived from Nonc- mutative Geometry Chapter3. New Directions in
Noncommutative Geometry and Mathema- cal Physics During the
conference the close interaction between mathematicians and
mathematical physicists turned out to be quite fruitful and
enlightening for both sides. Similarly, it is hoped that the
proceedings presented here will be useful for mathematicians
interested in basic physical questions and for physicists aiming at
a more conceptual understanding of classical and qu- tum ?eld
theory from a novel mathematical point of view.
The outcome of a close collaboration between mathematicians and mathematical physicists, these Lecture Notes present the foundations of A. Connes noncommutative geometry, as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.
This book provides a comprehensive exposition of M-ideal theory, a
branch ofgeometric functional analysis which deals with certain
subspaces of Banach spaces arising naturally in many contexts.
Starting from the basic definitions the authors discuss a number of
examples of M-ideals (e.g. the closed two-sided ideals of
C*-algebras) and develop their general theory. Besides,
applications to problems from a variety of areas including
approximation theory, harmonic analysis, C*-algebra theory and
Banach space geometry are presented. The book is mainly intended as
a reference volume for researchers working in one of these fields,
but it also addresses students at the graduate or postgraduate
level. Each of its six chapters is accompanied by a
Notes-and-Remarks section which explores further ramifications of
the subject and gives detailed references to the literature. An
extensive bibliography is included.
|
|