Multilocal fermionization

TL;DR

This paper introduces an isomorphism between single and multiple real chiral Fermi fields, revealing multilocal symmetries and unifying recent findings on free Bose-Fermi representations and modular theory in quantum field theory.

Contribution

It provides a new isomorphism that preserves the vacuum state, enabling multilocal symmetries and explaining recent results in free field representations.

Findings

Established an isomorphism between one and n real chiral Fermi fields.

Revealed multilocal symmetries generated by multilocal currents.

Unified explanations for free Bose-Fermi field representations and modular theory results.

Abstract

We present a simple isomorphism between the algebra of one real chiral Fermi field and the algebra of n real chiral Fermi fields. This 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, and on the modular theory of the free Fermi algebra in disjoint intervals.