Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators

TL;DR

This paper develops a gauge-invariant framework for magnetic translation operators, embedding them in so(3,1) symmetry, and derives Curtright-Zachos generators, revealing new algebraic insights.

Contribution

It introduces a gauge-invariant formulation of magnetic translations and connects them with so(3,1) conformal symmetry, deriving CZ generators from this structure.

Findings

Gauge-invariant magnetic translation operators formulated.

Embedding of GMT operators within so(3,1) algebra demonstrated.

Derivation of Curtright-Zachos generators from gauge-invariant operators.

Abstract

We propose a gauge-invariant formulation of magnetic translation (GMT) operators, eliminating the gauge dependence that conventional definitions suffer from due to specific gauge choices. We extend this framework by incorporating so(3,1) conformal symmetry, demonstrating how GMT operators can be naturally embedded within this algebraic structure. We then show the fundamental role of sim(2) duality between pseudo-dilatation and pseudo-angular momentum operators in constructing GMT operators. A key result of this approach is the derivation of the Curtright-Zachos (CZ) generators from gauge-invariant so(3,1) operators, providing a novel perspective on their algebraic properties such as the relationship between FFZ internal symmetry and sim(2) duality.