TFADPV016 Topological solitons

Institute of physics in Opava
winter 2022
Extent and Intensity
0/0/0. Type of Completion: dzk.
Guaranteed by
RNDr. Filip Blaschke, Ph.D.
Institute of physics in Opava
Prerequisites
A good knowledge of classical field theory and the basics of quantum field theory and Lie group theory is assumed, namely, the following ones:
• Lagrangian and Hamiltonian formalism for classical fields,
• Noether's theorem and conservation laws,
• Lorentz group and its representation,
• Dirac's equation and its solution,
• Quantization of free fields,
• Representation of unitary and orthogonal groups.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The goal of the study is to gain deep insight into the issue of topological solitons in classical field theory with applications to quantum field theory, particle physics and condensed matter. Core points of study are domain walls, vortices, magnetic monopoles and instantons. Emphasis is also partly placed on the connection with so-called supersymmetry, and how these solitons are connected through dimensional reduction.
Learning outcomes
Depends on advanced content (see Content).
Syllabus
  • The basic content of the subject is made up of parts:
  • • Kinks in scalar field theory with "double-well" potential and their collisions,
  • • Supersymmetry in 1+1 dimensions and BPS kinks, kinks with fermion number, Jackiw-Rebbi mechanism,
  • • Magnetic vortices in 2+1 dimensions in the Abelian theory of superconductivity, BPS limit, "Moduli-matrix" formalism,
  • • "Lumps" in 2+1 dimensions, topological degree map, integrable case = CP1 model, lump stabilization methods,
  • • Magnetic monopole as a singularity of the electromagnetic field. Dirac quantization condition, Dirac string,
  • • Magnetic monopole in SU(2) non-Abelian gauge theory, BPS limit and exact single monopole solution,
  • • Instantons in Euclidean SU(2) Yang-Mills theory, BPS solutions, construction of multi-instanton solutions.
  • The more advanced content of the subject is made up of parts that are selected for the content of the subject as part of the individual study plan in such a way that they are directly related to the thematic focus of the dissertation and at the same time appropriately complement the parts of other mandatory optional subjects of the student's individual study plan. This can be, for example, the following oness:
  • • Exact solution of multi-kinks in the sine-Gordon model,
  • • Duality between sine-Gordon and massive Thirring models at the quantum level,
  • • Domain walls in multidimensional supersymmetric theories, exact solution for "wall-junctions",
  • • Modules of the approximation of the dynamics of lumps, Incompleteness of geodesics and instability,
  • • Exact supersymmetric models with domain walls and vortex-strings, "Boojum" as a trapped magnetic monopole,
  • • Nahm's equations and construction of multi-monopole BPS solutions,
  • • Hierarchy of solitons in the Yang-Higgs-Mills model through dimensional reduction.
Literature
  • Manton, N., Sutcliffe, P. Topological solitons, Cambridge University Press, 2004
  • Nakahara, M. Geometry, Topology and Physics, IOP Publishing Ltd., 2003
  • Shnir, Y. Magnetic Monopoles, Springer-Verlag Berlin Heidelberg, 2005
Teaching methods
Consultation
Assessment methods
exam
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms winter 2021, winter 2023, winter 2024.
  • Enrolment Statistics (winter 2022, recent)
  • Permalink: https://is.slu.cz/course/fu/winter2022/TFADPV016