Fermion to Boson Mapping

TL;DR

This paper introduces an extension of the fermion algebra on the lattice, incorporating discrete space invariance, resulting in a new algebraic structure that combines fermionic and spatial symmetries.

Contribution

It extends the enveloping algebra of fermions to include lattice space invariance, creating a new algebraic framework for fermions on the lattice.

Findings

Extended algebra X includes space symmetry as a factor.

The algebra X/D_{n} equals the space group.

Provides a new mathematical structure for lattice fermions.

Abstract

The enveloping algebra,$D_{n}$,of fermions is extended on the lattice to include the discrete space invariance.This extended algebra,denoted X, has the space symmetry as a factor : $X/D_{n}$ = space group.