Symmetries of field theories on the non-commutative plane
P. A. Horvathy, L. Martina, and P.C. Stichel
TL;DR
This paper reviews recent advances in understanding symmetries of non-relativistic field theories on the non-commutative plane, highlighting how Galilean invariance constrains interactions and affects vortex solutions.
Contribution
It demonstrates that Galilean invariance imposes strong restrictions on interactions and reveals a geometrical phase in vortex solutions coupled to Chern-Simons fields.
Findings
Galilean invariance restricts admissible interactions
A geometrical phase appears in vortex solutions
Galilei boosts transform vortex solutions with a phase
Abstract
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a scalar field is coupled to a Chern - Simons gauge field, a geometrical phase emerges for vortex - like solutions, transformed by Galilei boosts.
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