ویراساینس.
سند علمی

Lectures on Topological Quantum Field Theory

J. M. F. Labastida, Carlos Lozano

چکیده

In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N = 2 supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory obtained from the application of results based on duality for N = 2 supersymmetric Yang-Mills theories. This involves a description of the computation of Donaldson invariants in terms of Seiberg-Witten invariants. Generalizations of Donaldson-Witten theory are reviewed, and the structure of the vacuum expectation values of their observables is analyzed in the context of duality for the simplest case. Lectures given at the workshop “Trends in Theoretical Physics”, CERN-Santiago de Compostela-La Plata Meeting, held in La Plata, Argentina, April 28-May 6 1997.

اسناد مشابه

  • Undergraduate Lecture Notes in Topological Quantum Field Theory

    سند علمی۲۰۰۸Vladimir G. Ivancevic, Tijana T. Ivancevic

    These third–year lecture notes are designed for a 1–semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second–year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagneti

  • Duality in the Context of Topological Quantum Field Theory

    سند علمی۱۹۹۹J. M. F. Labastida, Carlos Lozano

    We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and their relation to the Donaldson invaria

  • Schwarz Type Topological Quantum Field Theories

    سند علمی۲۰۰۵R. K. Kaul, T. R. Govindarajan

    Topological quantum field theories (TQFT) provide powerful tools to probe topology of manifolds, specifically in low dimensions[1, 2, 3, 4, 5]. This is achieved by incorporating very large gauge symmetries in the theory which lead to gauge invariant sectors with only topological

  • The Classification of Topological Quantum Field Theories in Two Dimensions

    سند علمی۲۰۱۴Geoffrey Lee, Jacob Lurie

    The goal of this thesis is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented e

  • Duality and Topological Quantum Field Theory *

    سند علمی۱۹۹۷J. M. F. Labastida, M. Mariño

    We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Don-aldson invariants in terms of Seiberg-Witten invariants using recent results in N = 2 supersymmetric gauge theory. A brief ac

  • Axiomatic Topological Quantum Field Theory

    سند علمی۲۰۱۲Romano Bianca

    This dissertation provides an introduction to the ideas employed in topological quantum field theory. We illustrate how the field began by considering knot invariants of three-manifolds and demonstrating the consequences of defining such a theory axiomatically. The ideas of categ