2000/06/30 by Wellington da Cruz · 2 citations
Mathematics · Physics and Astronomy · #Central charge #Charge (physics) #Combinatorics #Conformal field theory #Conformal map #Connection (principal bundle) #Duality (order theory) #Fractal #Geometry #Luttinger liquid #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum field theory #Quantum many-body systems #Quantum mechanics #Quasiparticle #Superconductivity #Theoretical and Computational Physics #cond-mat.mes-hall #hep-th #quant-ph
paper · pdf · doi:10.1088/0953-8984/12/44/101
published in Journal of Physics Condensed Matter 12(44), L673-L675 (IOP Publishing) · Latex, 5 pages, references added (To appear in J. of Physics: Cond. Mat.)
arxiv created 2000/10/05 · openalex publication_date 2000/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter = ν + 1 which is identified with the controlling parameter e -2φ of the Luttinger model. In this way, a bosonic system characterized by a fractal index i f [ h ] = i f [2] = 1 is considered in a conformal field theory with central charge c [ν = 0] = 1 = i f [2] with a compactified radius R = 1/ 1/2 = 1. Thus, we have a mapping of a bosonic theory to a fermionic one and vice versa, i.e. the duality symmetry = 3- h of the universal class h of fractons defined in the interval 1< h <2 is satisfied.