# Antiparticles as particles: QED$_{2+1}$ and composite Fermions at $\nu = \frac{1}{2}$

## TL;DR

This paper introduces a continuum operator map in 3D QED that swaps particles and antiparticles, providing a new realization of composite fermions at half-filling and demonstrating dualities in magnetic fields.

## Contribution

It presents a novel nonlocal operator map that inverts particle roles in 3D QED, connecting to Son's composite fermion theory at  = 1/2.

## Key findings

- Provides a continuum realization of Son's composite fermions
- Demonstrates inversion of Landau levels and duality in magnetic fields
- Connects gauge-invariant formulations to particle-antiparticle roles

## Abstract

We present a continuum operator map that inverts the role of particles and antiparticles in three dimensional QED. This is accomplished by the attachment of specific holomorphic Wilson lines to Dirac fermions. We show that this nonlocal map provides a continuum realization of Son's composite fermions at $\nu = \frac{1}{2}$. The inversion of Landau levels and the Dirac-cone--composite-Fermion duality is explicitly demonstrated for the case of slowly varying magnetic fields. The role of Maxwell-terms as well as the connection of this construction to a gauge-invariant formulation of 3D gauge theories is also elaborated upon.