Multilocal Fermionization |
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Authors: | Karl-Henning Rehren Gennaro Tedesco |
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Institution: | 1. Institut für Theoretische Physik, Universit?t G?ttingen, Friedrich-Hund-Platz 1, 37077, G?ttingen, Germany 2. Courant Research Centre “Higher Order Structures in Mathematics”, Universit?t G?ttingen, Bunsenstr. 3–5, 37073, G?ttingen, Germany
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Abstract: | 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) |
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