TL;DR
This paper explores the structure of momentum space in Snyder algebra, revealing its isomorphism to SO(3) and the existence of two distinct lattice structures that support continuous symmetries.
Contribution
It demonstrates the isomorphism between momentum space and SO(3), and identifies two different lattice structures compatible with Snyder algebra.
Findings
Momentum space is isomorphic to SO(3).
Two distinct lattice structures of space exist.
Continuous rotations and translations are unitarily implementable.
Abstract
We examine basis functions on momentum space for the three dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces. This implies the existence of two distinct lattice structures of space, on which continuous rotations and translations are unitarily implementable.
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