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

from Part III - Other Spins or Statistics; General Relativity

Published online by Cambridge University Press:  04 March 2019

Horaƫiu Năstase
Affiliation:
Universidade Estadual Paulista, São Paulo
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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.

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Publisher: Cambridge University Press
Print publication year: 2019

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