Mathematics

Differential Geometry and Physics

Author: Mo-Lin Ge

Publisher: World Scientific

ISBN:

Category: Mathematics

Page: 522

View: 482

This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.
Mathematics

The Geometry and Physics of Knots

Author: Michael Francis Atiyah

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 78

View: 156

Deals with an area of research that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.
Mathematics

Geometry and Physics

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 217

View: 720

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Mathematics

Discrete Integrable Geometry and Physics

Author: Alexander I. Bobenko

Publisher: Oxford University Press, USA

ISBN:

Category: Mathematics

Page: 370

View: 769

Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.

Geometry and Physics: Volume 2

Author: Andrew Dancer

Publisher:

ISBN:

Category:

Page: 352

View: 893

These texts contain 29 articles that cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics
D-branes

Noncommutative Geometry and Physics 3

Author: Giuseppe Dito

Publisher: World Scientific

ISBN:

Category: D-branes

Page: 536

View: 947

Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
Mathematics

Geometry and physics

Author: Asim Orhan Barut

Publisher: Humanities Pr

ISBN:

Category: Mathematics

Page: 123

View: 964

Mathematics

Geometry and Physics

Author: H. Pedersen

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 768

View: 847

"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."