Extended Space Duality in the Noncommutative Plane
Subir Ghosh (Indian Statistical Institute)
TL;DR
This paper develops a unified framework for studying various noncommutative structures in planar quantum mechanics by embedding a noncommutative harmonic oscillator into an extended space, revealing dualities among different NC formulations.
Contribution
It introduces a Master model using Batalin-Tyutin embedding that systematically explores different noncommutative structures in a unified manner.
Findings
Different gauge choices produce distinct NC structures
The framework reveals dualities between different noncommutative theories
All NC structures can be studied systematically within the extended space
Abstract
Non-Commutative (NC) effects in planar quantum mechanics are investigated. We have constructed a {\it{Master}} model for a noncommutative harmonic oscillator by embedding it in an extended space, following the Batalin-Tyutin \cite{bt} prescription. Different gauge choices lead to distinct NC structures, such as NC coordinates, NC momenta or noncommutativity of a more general kind. In the present framework, all of these can be studied in a unified and systematic manner. Thus the dual nature of theories having different forms of noncommutativity is also revealed.
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