Geometry and Physics

ISBN-13: 9783642005404 / Angielski / Twarda / 2009 / 232 str.

Ja1/4rgen Jost

Opis

"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. Jurgen 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."

Recenzje

From the reviews:

"This book is a fresh presentation ... of field theory, using a modern mathematical language. ... This covers some interesting actual subjects concerning a mathematical model formulation of high-energy particles physics. ... this book can be very useful for beginners. ... can be recommended to the attention of all students and scientists that aim to find a short direct introduction in the field theory of particle physics." (Agostino Prástaro, Zentralblatt MATH, Vol. 1176, 2010)

"It's an extremely unusual book on a number of counts. ... I find the book eminently readable, inpact spellbinding. ... I am happy to recommend Jost's Geometry and Physics to any one with enough mathematics under his belt not to wince at a pair of phrases ... . Read and enjoy this fascinating book, delve deeper where you wish ... ." (Michael Berg, The Mathematical Association of America, February, 2010)

"In this book the author gives an overview of the relation between geometry and physics. ... This work is an excellent and thoughtful review of one of the most important subjects in contemporary theoretical physics. ... The book is very well written and I would recommend it to everyone who wants a good introduction to the subject as well as to theoreticians and mathematicians who work on the boundary between mathematics and physics." (Guglielmo Fucci, Mathematical Reviews, Issue 2010 k)

Spis treści

1.Geometry.- 1.1.Riemannian and Lorentzian manifolds.- 1.2.Bundles and connections.- 1.3.Tensors and spinors.- 1.4.Riemann surfaces and moduli spaces.- 1.5.Supermanifolds.- 2.Physics.- 2.1.Classical and quantum physics.- 2.2.Lagrangians.-2.3.Variational aspects.- 2.4.The sigma model.- 2.5.Functional integrals.- 2.6.Conformal field theory.- 2.7.String theory.- Bibliography.- Index.

Blurb

"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.