{"product_id":"supermanifolds-cambridge-monographs-on-mathematical-physics-9780521423779","title":"Supermanifolds (Cambridge Monographs on Mathematical Physics)","description":"\u003cp\u003eThis is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds  including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassman variables)  Berezin integration  supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds  with an account of super-analogs of Lie derivatives  connections  metric  curvature  geodesics  Killing flows  conformal groups  etc. The book goes on to discuss the theory of super Lie groups  super Lie algebras  and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The book then turns to applications. Chapter 5 contains an account of the Peierals bracket for superclassical dynamical systems  super Hilbert spaces  path integration for fermionic quantum systems  and simple models of BoseFermi supersymmetry. The sixth and final chapter  which is new in this revised edition  examines dynamical systems for which the topology of the configuration supermanifold is important. A concise but complete account is given of the pathintegral derivation of the ChernGaussBonnet formula for the EulerPoincar characteristic of an ordinary manifold  which is based on a simple extension of a point particle moving freely in this manifold to a supersymmetric dynamical system moving in an associated supermanifold. Many exercises are included to complement the text.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45651901841461,"sku":"ByrdShop_0521423775","price":82.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780521423779.jpg?v=1781844664","url":"https:\/\/atxbooks.com\/products\/supermanifolds-cambridge-monographs-on-mathematical-physics-9780521423779","provider":"ATX Books","version":"1.0","type":"link"}