Duality and an Operator Realization for the Fermi-Bose Transmutation in 3+1 Dimensions

TL;DR

This paper provides an explicit operator framework demonstrating Fermi-Bose transmutation in 3+1 dimensions through duality and topological interactions in a Maxwell-Higgs system.

Contribution

It introduces a novel operator realization for statistical transmutation in 3+1D using duality between electromagnetic and Kalb-Ramond descriptions.

Findings

Commutation relations imply dual algebra and generalized statistics.

In the local limit, only Fermi or Bose statistics are possible.

Explicit realization of Fermi-Bose transmutation in 3+1D.

Abstract

We consider the Maxwell-Higgs system in the broken phase, described in terms of a Kalb-Ramond field interacting with the electromagnetic field through a topological coupling. We then study the creation operators of states which respectively carry a point charge and a closed magnetic string in the electromagnetic language or a point topological charge and a closed Kalb-Ramond charged string in the Kalb-Ramond dual language. Their commutation relation is evaluated, implying they satisfy a dual algebra and their composite possesses generalized statistics. In the local limit where the radius of the string vanishes, only Fermi or Bose statistics are allowed. This provides an explicit operator realization for statistical transmutation in 3+1D.