Fermions without fermi fields

TL;DR

This paper demonstrates that any fermionic Hamiltonian can be represented without explicit fermion fields, maintaining locality and potentially explaining fermionic excitations without fundamental fermion fields.

Contribution

It generalizes previous work by showing all fermionic Hamiltonians can be represented with local operators without fermion fields, applicable to Majorana fermions and mitigating fermion doubling.

Findings

Fermionic Hamiltonians can be represented without fermion fields.

Locality is preserved in the new representation.

The approach applies to Majorana fermions and addresses fermion doubling.

Abstract

It is shown that an arbitrary Fermion hopping hamiltonian can be represented by a system with no fermion fields, generalising earlier results by M. Levin & X.G. Wen [Phys Rev B 67, 245316 (2003)]. All the operators in the hamiltonian of resulting description obey the principle of locality, that operators associated with different sites commute, despite the system having excitations obeying Fermi statistics. Whilst extra conserved degrees of freedom are introduced, they are all locally identified in the representation obtained. The same methods apply to Majorana (half) fermions, which for cartesian lattices mitigate the Fermion Doubling Problem. The generality of these results suggests that the observation of Fermion excitations in nature does not demand that anticommuting Fermion fields are fundamental.