Quantum Dynamics on the three-dimensional q-deformed Euclidean Space

2020/04/11 by Wachter, Hartmut
#16T05 (Primary) #81R50 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2004.05444

Abstract

I extend the three-dimensional q-deformed Euclidean space by a time element and discuss the algebraic structure of this quantum space together with its differential calculi. Using the star-product formalism, I will give basic operations of q-deformed analysis for the q-deformed Euclidean space with a time element. I show that the time-evolution operator of a quantum system living in the q-deformed Euclidean space is of the same form as in the undeformed case. The reasonings also show that the well-known methods of quantum dynamics apply to quantum systems living in the q-deformed Euclidean space.

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