Non-Commutative Time, the Quantum Hall Effect and Twistor Theory
Mesoscale and Nanoscale Physics
2007-05-23 v1
Abstract
It is proposed that Maxwell theory, with a topological term, in four non-commutative dimensions, where the co-ordinates obey the Heisenberg algebra, is an umbrella theory for the description of the two-dimensional Quantum Hall Effect (following the fluidic approach of Susskind and Polychronakos), the twistor analyses of self-dual gravity, solitons and instantons and the twistor theory of isolated horizons in space-time. Applied to the Quantum Hall case, the underlying metric is Lorentzian: two canonically conjugate co-ordinates are spatial, the other two co-ordinates naturally are null and represent time and a conjugate energy variable.
Cite
@article{arxiv.cond-mat/0401224,
title = {Non-Commutative Time, the Quantum Hall Effect and Twistor Theory},
author = {Dana Mihai and George Sparling and Philip Tillman},
journal= {arXiv preprint arXiv:cond-mat/0401224},
year = {2007}
}