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Abstract: We develop the physics of dual kappa Poincare algebra, which we will calldual DSR. First, we show that the dual kappa Poincare algebra is isomorphic tode Sitter algebra and its spactime is essentially de Sitter spacetime. Second,we show how to derive the coproduct rules for Beltrami and conformalcoordinates of de Sitter spacetime. It follows from the current literature onde Sitter relativity that the speed of light c and the de Sitter length are thetwo invariant scales of the physics of dual kappa Poincare algebra. Third, wederive the Casimir invariant of the dual kappa Popincare algebra and use thisto derive an expression for the speed of light, our fourth result. Fifth, thefield equation for the scalar field is derived from the Casimir invariant. Theresults for the coordinate speed of light and the scalar field theory are thesame as in de Sitter theory in the planar coordinate basis. Thus, we have shownthat the physics of dual kappa Poincare algebra in the dual bicrossproductbasis, which can be apprpriately called dual DSR, is essentially de Sitterrelativity. Sixth, we argue the existence of an observer-independent minimummomentum. Seventh, we argue heuristically that the existence of minimummomentum will lead to a dual generalized uncertainty principle. Finally, wenote that dual DSR is not a quantum theory of spacetime but a quantum theory ofmomenta.

Author: Jose A. Magpantay

Source: https://arxiv.org/

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