The University of Queensland

Centre for Mathematical Physics

SEMINAR

Speaker: Xin Liu, Mathematics, UQ

Title: Gauge Potential Decomposition and Geometric Description for Topological Defects

10am, Thursday 4^th May, 2006

Priestley Blding, room 140

Abstract:

It is known that many topologically invariant characteristic classes are constructed with gauge field tensors, while the latter are constructed with gauge potentials. So it is natural to expect: if gauge potentials are decomposed in terms of basic fields on the manifold (i.e. the wave functions of quantum-mechanical systems), characteristic classes can also be expressed by these basic fields. The point of this idea is that it provides a direct path to study the singularities that reside in the distribution of basic fields and lead to topological defects. From this point of view we will introduce the gauge potential decomposition and the topological currents, and show that different dimensional topological defects (such as instantons, monopoles and vortex lines) can be derived from topological currents.

Furthermore, since knot-like lines are an important category of vortex lines, we focus on the knot structures originating from the Abelian Chern-Simons action. Actually this action can be written as a family of knots which are characterized by their linking and self-linking numbers. Moreover, it is shown that this action is preserved during branching processes of knots, and the linking between different knots can be regarded as interactions transmitted by topological intermediate particles.

All interested are invited to attend.

Enquiries to Katrina Hibberd email: keh@maths.uq.edu.au