String Theory And Noncommutative Geometry

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. This Book Provides A Systematic, Comprehensive And Up-to-date Account Of The Recent 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 Recently Aroused Renewed 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 Book Comprises Nine Chapters. Chapter 1 Gives A Sound Mathematical Ntroduction To Non-commutative Spacetime Coordinates In Classical And Quantum Physics. In Chapter 2, Non-commutativity In A String Theory Is Discussed At A Pedagogic Level. Chapter 3 Deals With An Aribitrary D-brane Dynamics And Chapter 4 Describes The Non-commutative Gauge Theories On A D-brane. In Chapters 5-9, Non-commutative Quantum Field Theory (ncqft) Is Addressed. In Particular, Chapter 5 Deals With The Real Scalar Ncqft, Chapter 6 With That Of Complex Scalar Field, Chapter 7 Describes Spontaneous Symmetry Breaking In Scalar Ncqft, Chapter 8 Deals With The U(1) Gauge Theory And Chapter 9 With Su(n) Gauge Theories.students Will Find This Book Useful As A Bridge Between String And Field Theories. In Addition, It Will Prove Invaluable For Interdisciplinary Areas Of Study.