{"id":1043,"date":"2012-02-04T18:02:19","date_gmt":"2012-02-04T17:02:19","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=1043"},"modified":"2012-02-04T18:02:19","modified_gmt":"2012-02-04T17:02:19","slug":"topology-and-geometry-for-physicists-by-c-nash-s-sen","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2012\/02\/04\/topology-and-geometry-for-physicists-by-c-nash-s-sen\/","title":{"rendered":"Topology and geometry for physicists, by C. Nash & S. Sen"},"content":{"rendered":"\n\n\n
\"\"Topology and Geometry for Physicists<\/a>\"\"\n<\/td>\n\n

Geometry and topology are now a well established tools in the theoretical physicists tool kit. Topology and geometry for physicists<\/em> by C. Nash & S. Sen gives a very accessible introduction to the subject without getting bogged down with mathematical rigour. <\/p>\n

Examples from condensed matter physics, statistical physics and theoretical high energy physics appear throughout the book. <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

However, one obvious topic missing is general relativity. As the authors state, good books on geometry & topology in general relativity existed at the time of writing.<\/p>\n

The first 8 chapters present the key ideas of topology and differential geometry.<\/p>\n

Chapter 1 discusses basic topology. Topics include homomorphisms, homotopy, the idea of topological invariants, compactness and connectedness. The reader is introduced to “topological thinking”.<\/p>\n

Manifolds are the subject of Chapter 2. Topics include: the definition of manifolds, orientablilty, calculus on manifolds and differential structures. <\/p>\n

Chapter 3 discusses the fundamental group. Topics include: the definition of the fundamental group, simplexes, triangulation and the fundamental group of a product of spaces. <\/p>\n

Chapter 4 moves on to the homology group. Topics include: the definition of homology groups, relative homology, exact sequences, the Kunneth formula and the Poincare-Euler formula. <\/p>\n

The higher homotopy groups are the subject of Chapter 5. Topics covered include: the definition of higher homotopy groups, the abelian nature of higher homotopy groups and the exact homotopy sequence. <\/p>\n

The de Rham cohomology of a manifold is the subject of Chapter 6. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. <\/p>\n

Chapter 7 presents the core concepts of differential geometry. Topics here include: fibre bundles, sections, the Lie derivative, connections on bundles, curvature, parallel transport, geodesics, the Yang-Mills connection and characteristic classes.<\/p>\n

Chapter 8 outlines Morse theory. Topics include: the Morse inequalities and the Morse lemma. Connection with physics is established via symmetry breaking selection rules in crystals.<\/p>\n

The next two chapters look at application in physics of some of the ideas presented earlier in the book.<\/p>\n

Defects and homotopy theory is the subject of Chapter 9. Topics include: planar spin in 2d, ordered mediums and the stability of defects theorem.<\/p>\n

Chapter 10 discusses instantons and monopoles in Yang-Mills theory. Topics here include: instantons, instanton number & the second Chern class, instantons in terms of quaternions, twistor methods, monopoles and the Aharanov-Bohm effect. <\/p>\n

Paperback:<\/strong> 311 pages
\nPublisher:<\/strong> Academic Press Inc; New edition edition (Jun 1987)
\nLanguage <\/strong>English
\nISBN-10:<\/strong> 0125140819
\nISBN-13:<\/strong> 978-0125140812<\/p>\n\n\n\n
\"\"<\/td>\n\n

The book has also been reprinted by Dover Books in 2011.<\/p>\n

Paperback:<\/strong> 311 pages
\nPublisher:<\/strong> Dover Publications Inc.; Reprint edition (17 Feb 2011)
\nLanguage<\/strong> English
\nISBN-10:<\/strong> 0486478521
\nISBN-13:<\/strong> 978-0486478524\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Topology and Geometry for Physicists Geometry and topology are now a well established tools in the theoretical physicists tool kit. Topology and geometry for physicists by C. Nash & S. Sen gives a very accessible introduction to the subject without getting bogged down with mathematical rigour. Examples from condensed matter physics, statistical physics and theoretical … Continue reading Topology and geometry for physicists, by C. Nash & S. Sen<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1043","post","type-post","status-publish","format-standard","hentry","category-book-reviews"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=1043"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1043\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=1043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=1043"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=1043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}