Dressed vs. Pairwise States, and the Geometric Phase of Monopoles and Charges

TL;DR

This paper constructs and analyzes dressed multi-particle states with electric and magnetic charges, revealing their transformation properties, geometric phases, and implications for spin-statistics, advancing understanding in quantum field theory and gauge symmetries.

Contribution

It introduces a new quantum field theoretic approach to dressed states with monopoles and charges, deriving geometric phases and spin-statistics relations.

Findings

Dressed states transform under the pairwise little group.

Finite Lorentz transformation shifts have a geometric interpretation.

Fermionic states can be constructed from bosonic constituents.

Abstract

We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helcity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.