Topological Concepts in Gauge Theories

Abstract

In these lecture notes, an introduction to topological concepts and methods in studies of gauge field theories is presented. The three paradigms of topological objects, the Nielsen-Olesen vortex of the abelian Higgs model, the 't Hooft-Polyakov monopole of the non-abelian Higgs model and the instanton of Yang-Mills theory, are discussed. The common formal elements in their construction are emphasized and their different dynamical roles are exposed. The discussion of applications of topological methods to Quantum Chromodynamics focuses on confinement. An account is given of various attempts to relate this phenomenon to topological properties of Yang-Mills theory. The lecture notes also include an introduction to the underlying concept of homotopy with applications from various areas of physics.

Lecture notes

References in corpus (3)

• The Confinement Problem in Lattice Gauge Theory
• Inverse melting of the vortex lattice
• Scalar Glueball Mass Reduction at Finite Temperature in SU(3) Anisotropic Lattice QCD

Cited by in corpus (5)

• Confining Effective Theories Based on Instantons and Merons
• "Discrete" vacuum geometry as a tool for Dirac fundamental quantization of Minkowskian Higgs model
• Topological charge fluctuations in the Glasma
• Nontrivial topological dynamics in Minkowskian Higgs model quantized by Dirac
• Undergraduate Lecture Notes in Topological Quantum Field Theory