1997/05/31 by Izumi Tsutsui, Hiroyuki Kobayash, Shogo Tanimura +1 · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00759-1
published as Nucl.Phys. B514 (1998) 667-687 · 24 pages, Plain Tex, 1 Postscript figure included using epsf, Minor changes in revised version
arxiv created 1997/07/28 · openalex publication_date 1998/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Hopf term in the 2 + 1 dimensional O(3) nonlinear sigma model, which is known to be responsible for fractional spin and statistics, is re-examined from the viewpoint of quantization ambiguity. It is confirmed that the Hopf term can be understood as a term induced quantum mechanically, in precisely the same manner as the θ-term in QCD. We present a detailed analysis of the topological aspect of the model based on the adjoint orbit parametrization of the spin vectors, which is not only very useful in handling topological (soliton and/or Hopf) numbers, but also plays a crucial role in defining the Hopf term for configurations of nonvanishing soliton numbers. The Hopf term is seen to arise explicitly as a quantum effect which emerges when quantizing an S1 degree of freedom hidden in the configuration space.