English

Pure 4-geometry of quantum magnetic spin matter from Kondo effect

High Energy Physics - Theory 2011-07-05 v1 Other Condensed Matter General Relativity and Quantum Cosmology

Abstract

We determine a smooth Euclidean 4-geometry on R^4 from quantum interacting spin matter like in the multichannel Kondo effect. The CFT description of both: the kk-channel Kondo effect of spin magnetic impurities quantum interacting with spins of conducting electrons and exotic smooth R^4, by the level kk WZW model on SU(2), indicates the relation between smooth R^4's and the quantum matter. We propose a model which shows: exotic smooth R^4_k generates fermionic fields via the topological structure of Casson handles and when this handle is attached to some subspace A of R^4 these fermions represent electrons bounded by the magnetic impurity. Thus the Kondo bound state of kk conducting electrons with magnetic impurity of spin ss is created like in the low temperature Kondo effect. Then the quantum character of the interactions is encoded in 4-exoticness. The complexity as well the number of Casson handles correspond to the number of channels in the Kondo effect. When the smoothness structure is the standard one, no quantum interactions are carried on by standard R^4.

Keywords

Cite

@article{arxiv.1107.0650,
  title  = {Pure 4-geometry of quantum magnetic spin matter from Kondo effect},
  author = {T. Asselmeyer-Maluga and J. Krol},
  journal= {arXiv preprint arXiv:1107.0650},
  year   = {2011}
}

Comments

7 pages, no figures