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Abstract: Based on a linear realization formulation of a quantum relativity - theproposed relativity for quantum `space-time-, we introduce thePoincar\-e-Snyder relativity and Snyder relativity as relativities in betweenthe latter and the well known Galilean and Einstein cases. We discuss how thePoincar\-e-Snyder relativity may provide a stronger framework for thedescription of the usual Einstein relativistic quantum mechanics and beyond.In particular, we discuss a geometric quantization picture through the U1central extension of the relativity group, which had been establish to workwell for the Galilean case but not for the Einstein case. We discusssimilarities and differences between our Poincar\-e-Snyder picture with a stillnot fully understood $\sigma$ variable as the `evolution- parameter and someuse of an invariant time or the proper time parameter in some earlierformulations with very similar mathematical structure. The study is a firststep towards the investigation of physics of the $\sigma$ variable at thePoincar\-e-Snyder setting, plausible leading to experimental signatures to bestudied.



Author: Otto C. W. Kong, Hung-Yi Lee Nat'l Central U., Taiwan

Source: https://arxiv.org/



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