Search

Summary

The purpose of this chapter is to understand how quantum particles react to magnetic fields. There are a number of reasons to do be interested in this. First, quantum particles do extraordinary things when subjected to magnetic fields, including forming exotic states of matter known as quantum Hall fluids. But, in addition, magnetic fields bring a number of new conceptual ideas to the table. Among other things, this is where we first start to see the richness that comes from combining quantum mechanics with the gauge fields of electromagnetism.

Summary

We define Chern–Simons gauge fields in 2+1 dimensions, and the quantization of their “level” k. We show that the CS action in a material define a topological response, and gives an integer quantum Hall effect. We show how a CS field emerges, as a statistical field, in materials. We define anyons and show how they can appear from a CS field in the fractional Quantum Hall effect.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

9 - Particles in a Magnetic Field

Summary

33 - Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics

Summary

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

9 - Particles in a Magnetic Field

Summary

33 - Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics

Summary