Local Charged States of the Gauge Field in Three Dimensional Maxwell-Type Theories

TL;DR

This paper introduces gauge-invariant local operators for charged states in 2+1D Maxwell theories, exploring their physical relevance, topological sectors, and implications for bosonization.

Contribution

It presents a dual Maxwell theory with topological electric charge and constructs physical charged states in nontrivial topological sectors, extending QED concepts.

Findings

Charged operators can create physical states in topologically nontrivial sectors.

Existence of an order-disorder structure linking charges and magnetic flux.

Relevance for bosonization in 2+1D discussed.

Abstract

Gauge invariant local creation operators of charged states are introduced and studied in pure gauge theories of the Maxwell type in 2+1D. These states are usually unphysical because of the subsidiary condition imposed on the physical subspace by Gauss' law. A dual Maxwell theory which possesses a topological electric charge is introduced. Pure Electrodynamics lies in the sector where the topological charge identically vanishes. Charge bearing operators fully expressed in terms of the gauge field, however, can create physical states in the nontrivial topological sectors which thereby generalize QED. An order disorder structure exists relating the charged operators and the magnetic flux creating (vortex) operators, both through commutation rules and correlation functions. The relevance of this structure for bosonization in 2+1D is discussed.