Local bosonization of massive fermions in three spatial dimensions with rotation invariance

TL;DR

This paper demonstrates that fermionic operators obeying Fermi-Dirac statistics can emerge from a fully commuting bosonic field theory with string-like structures, preserving rotation symmetry and stability of the fermionic ground state.

Contribution

It introduces a novel bosonization approach in three spatial dimensions that reproduces massive Dirac fermion dynamics while maintaining rotation invariance.

Findings

Fermionic operators can emerge from bosonic string and loop configurations.

The model preserves rotation symmetry despite potential violations of relativistic invariance.

A stable fermionic ground state (Fermi sea) exists under certain conditions.

Abstract

In relativistic quantum field theory particles of half-integer spin must obey Fermi-Dirac statistics. Their quantum operators must anticommute at spacelike separation in contrast to commuting physical observables. We show that Fermi-Dirac spin $1/2$ operators can be emergent in a fully commuting field theory forming directed strings and loops of spin 0 and 1 constituents, reproducing massive Dirac dynamics with background fields. Such underlying description may violate relativistic invariance but there are no manifest interactions at a distance and rotation symmetry remains preserved. We show that under some constraints on the model there exists a well-defined ground state -- Fermi sea that it is stable -- fermions cannot convert to bosons.