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Paper IPM / Physic / 17683  


Abstract:  
The Poincare symmetry can be contracted in two ways to yield the Galilei symmetry and the Carroll symmetry. The Schrodinger equation exhibits the Galilei symmetry and is a fundamental equation in Galilean quantum mechanics. However, the question remains: what is the quantum equation that corresponds to the Carroll symmetry? In this paper, we derive a novel equation, called the CarrollSchrÃ¶dinger equation, which describes the quantum dynamics in the Carrollian framework. We also introduce the CarrollSchrodinger algebra, which is a conformal extension of the centrally extended Carroll algebra, and show that it is the symmetry algebra of the CarrollSchrÃ¶dinger equation in two dimensions. We generalize our results to arbitrary dimensions and discuss some possible applications and extensions of our work.
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