Labastida / Marino Topological Quantum Field Theory and Four Manifolds

1. Auflage 2007
ISBN: 978-1-4020-3177-9
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 25, 234 Seiten, eBook

Reihe: Mathematical Physics Studies

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Zielgruppe

Research

Autoren/Hrsg.

Labastida, Jose

Marino, Marcos

Inhaltsverzeichnis

Topological Aspects of Four-Manifolds.- The Theory of Donaldson Invariants.- The Theory of Seiberg-Witten Invariants.- Supersymmetry in Four Dimensions.- Topological Quantum Field Theories in Four Dimensions.- The Mathai-Quillen Formalism.- The Seiberg-Witten Solution of N = 2 SUSY Yang-Mills Theory.- The u-plane Integral.- Some Applications of the u-plane Integral.- Further Developments in Donaldson—Witten Theory.