Topological Quantum Field Theory and Four Manifolds (Mathematical Physics Studies) [Hardcover]

Jose Labastida (Author), Marcos Marino (Author)

Book Description

ISBN-10: 1402030584 | ISBN-13: 978-1402030581 | Publication Date: April 29, 2005 | Edition: 1

The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the recent developments that have led to important applications in the context of the topology of four manifolds.

Editorial Reviews

Review

From the reviews of the first edition: "The present book … starts with a survey of important topological topics, then reviews the theories of Donaldson and Seiberg-Witten, and describes various aspects of supersymmetery … . Graduate students, post-docs and junior faculty interested in the interaction of physics and mathematics … will greatly benefit from this coherent treatment of the subject and the thorough evaluation of its virtues which is, to my knowledge, the first of its kind." (Gert Roepstorff, Zentralblatt MATH, Vol. 1087, 2006) "The book is written to be accessible either for physicists who want to know about the topological consequences of supersymmetric quantum field theory, or for mathematicians curious about where the links between Donaldson and Seiberg-Witten theory come from. For both groups it should be a good point of entry to the literature. … the authors manage to give an end-to-end treatment of the relation between Donaldson and Seiberg-Witten invariants, including a detailed computation of the formula connecting the two for manifolds of Seiberg-Witten simple type." (Andrew Neitzke, Mathematical Reviews, Issue 2006 f)

From the Back Cover

The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the recent developments that have led to important applications in the context of the topology of four manifolds.

Product Details

• Hardcover: 234 pages
• Publisher: Springer; 1 edition (April 29, 2005)
• Language: English
• ISBN-10: 1402030584
• ISBN-13: 978-1402030581
• Product Dimensions: 9.5 x 6.5 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #2,704,619 in Books (See Top 100 in Books)

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