Non-Commutative Geometry

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 introduction 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.

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• Non-Commutative Spacetime Coordinates
• Non-Commutativity in String Theory
• D-branes and Spacetime Non-Commutivity
• Gauge Theories on a D-brane
• Non-Commutative Real Scalar QFT
• Non-Commutative Complex Scalar QFT
• Spontaneous Symmetry Breaking in Non-Commutative scalar QFT
• Non-Commutative QED
• Non-Commutative QCD