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

Adam Bednorz

doi:10.1103/physrevd.98.036012

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.

Highlights

Relativistic quantum field theories, such as electrodynamics imply the existence of two kinds of fields: commuting bosons (Bose-Einstein operators) and anticommuting fermions (Fermi-Dirac operators). The former are realized for integer spins while the latter for half-integer
The proof of spin-statistics correspondence requires relativistic invariance and energy positivity [1,2,3,4,5] while relativity is a postulate imposed on quantum field theories [6]
The rough idea is that the fermions are emergent as endpoints of strings fluctuating in empty space. Even sacrificing relativity this concept is an interesting alternative to standard string theories, where fermions are always fundamental—not emergent

Summary

INTRODUCTION

Relativistic quantum field theories, such as electrodynamics imply the existence of two kinds of fields: commuting bosons (Bose-Einstein operators) and anticommuting fermions (Fermi-Dirac operators). The former are realized for integer spins while the latter for half-integer. The division into fermions and bosons remains in all modern theories, including standard model, string or superstring and M-theory [7,8,9,10] Some time ago it has been proposed a theory reducing fermions to composite states of bosons—string-nets—at very high energy/momentum scale [11,12]. We close the paper with the discussion of the high-energy deviations and proposed further development of the models

FERMIONS IN QUANTUM ELECTRODYNAMICS

DIRECTED STRING

BASIC HAMILTONIAN

ENDPOINTS DYNAMICS

RECONSTRUCTING DIRAC EQUATION

VIII. DISCUSSION