Letters in Mathematical Physics

, Volume 103, Issue 1, pp 19–36

Multilocal Fermionization

Open Access


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 


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany
  2. 2.Courant Research Centre “Higher Order Structures in Mathematics”Universität GöttingenGöttingenGermany

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