{"product_id":"9783662141090","title":"An Introduction to Noncommutative Spaces and Their Geometries","description":"\u003ch3\u003eLecture Notes in Physics Monographs\u003c\/h3\u003e\u003ch1\u003eAn Introduction to Noncommutative Spaces and Their Geometries\u003c\/h1\u003e\u003ch3\u003eGiovanni Landi\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eScience \/ Physics \/ Mathematical \u0026amp; Computational\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eThese lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.\r\nApplication to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.\r\nSome recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.\r\nThis book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e23 August 2014\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Berlin Heidelberg\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783662141090\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e207\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":51215649341580,"sku":"9783662141090","price":107.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783662141090.jpg?v=1783007953","url":"https:\/\/lateknightbooks.com\/products\/9783662141090","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}