Letters in Mathematical Physics

, Volume 103, Issue 1, pp 19-36

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Multilocal Fermionization

  • Karl-Henning RehrenAffiliated withInstitut für Theoretische Physik, Universität GöttingenCourant Research Centre “Higher Order Structures in Mathematics”, Universität Göttingen Email author 
  • , Gennaro TedescoAffiliated withInstitut für Theoretische Physik, Universität Göttingen


We present a simple isomorphism between the algebra of one real chiral Fermi field and the algebra of n real chiral Fermi fields. The isomorphism preserves the vacuum state. This is possible by a “change of localization”, and gives rise to new multilocal symmetries generated by the corresponding multilocal current and stress–energy tensor. The result gives a common underlying explanation of several remarkable recent results on the representation of the free Bose field in terms of free Fermi fields (Anguelova, arXiv:1112.3913, 2011; Anguelova, arXiv:1206.4026, 2012), and on the modular theory of the free Fermi algebra in disjoint intervals (Casini and Huerta, Class Quant Grav 26:185005, 2009; Longo et al., Rev Math Phys 22:331–354, 2010)

Mathematics Subject Classification



CAR algebra conformal field theory modular theory