Modern Differential Geometry for Physicists

Fülszöveg

Modern differential Geometry forPhysicists This edition of the invaluable text Modern Differential Geometry for Physicists contains ajn additional chapter that introduces somé of the basic ideas of generál topology needed ín differential geometry. A number of small corrections and additions have alsó been made. These lecture notes are the content of an introductory course on modern, coordinatefree differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Quantum Fields and Fundamental Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of generál relativity but alsó the theory of Yang-Mills fields, nonlinear sigma models and other types of noniinear field systems that... Tovább

Fülszöveg

Modern differential Geometry forPhysicists This edition of the invaluable text Modern Differential Geometry for Physicists contains ajn additional chapter that introduces somé of the basic ideas of generál topology needed ín differential geometry. A number of small corrections and additions have alsó been made. These lecture notes are the content of an introductory course on modern, coordinatefree differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Quantum Fields and Fundamental Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of generál relativity but alsó the theory of Yang-Mills fields, nonlinear sigma models and other types of noniinear field systems that feature in modern quantum field theory. The volume is divided into four parts: (i) introduction to generál topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure'', . which he develops from several different points of view - somé geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry. "This book is carefully written, and attention is paid to rigor and relevant details ... The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism." Mathematical Reviews "The mathematical notions are sprinkled with many remarks and hints of physical flavour; therefore, the text may be extremely valuable for those mathematics students interested in applications of differential geometry to other areas." Mathematics Abstracts Vissza