Non-commutative Geometry: A Perspective On String And Field Theories

A systematic and comprehensive account of developments in non-commutative geometry, at a pedagogical level. It does not go into the details of rigorous (advanced level) mathematical formulation of non-commutative geometry; rather, it restricts itself to the domain of strings and quantum fields. Since non-commutative geometry has aroused revived interest in open string theory, the author motivates the text from the viewpoint of a string theory. He begins with an introduction to the subject, explaining what one means by non-commutative geometry and why it is relevant to study such geometry, and discussing its possible origin in a string theory. The text comprises five chapters. Chapter 1 gives a mathematical introduction. In Chapter 2, non-commutativity in an open bosonic string theory is discussed with explicit calculations. Chapter 3 deals with non-commutative quantum fields, their dynamics and some of their interactions. In Chapter 4, some of the classical solutions of non-commutative string and field theories are discussed. Chapter 5 treats some applications of non-commutative theory. Students should find this book useful as a bridge between string and field theories. It should also prove useful for interdisciplinary areas of study.