2004/01/13 by Dana Mihai, Mihai, Dana, George Sparling +3
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.cond-mat/0401224
arxiv created 2004/01/13 · openalex publication_date 2004/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.