Dual DSR

Abstract

We develop the physics of dual kappa Poincare algebra, which we will call dual DSR. First, we show that the dual kappa Poincare algebra is isomorphic to de Sitter algebra and its spactime is essentially de Sitter spacetime. Second, we show how to derive the coproduct rules for Beltrami and conformal coordinates of de Sitter spacetime. It follows from the current literature on de Sitter relativity that the speed of light c and the de Sitter length are the two invariant scales of the physics of dual kappa Poincare algebra. Third, we derive the Casimir invariant of the dual kappa Popincare algebra and use this to derive an expression for the speed of light, our fourth result. Fifth, the field equation for the scalar field is derived from the Casimir invariant. The results for the coordinate speed of light and the scalar field theory are the same as in de Sitter theory in the planar coordinate basis. Thus, we have shown that the physics of dual kappa Poincare algebra (in the dual bicrossproduct basis), which can be apprpriately called dual DSR, is essentially de Sitter relativity. Sixth, we argue the existence of an observer-independent minimum momentum. Seventh, we argue heuristically that the existence of minimum momentum will lead to a dual generalized uncertainty principle. Finally, we note that dual DSR is not a quantum theory of spacetime but a quantum theory of momenta.

22 pages

References in corpus (14)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• A Generalized Uncertainty Principle in Quantum Gravity
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Non-commutative space-time of Doubly Special Relativity theories
• Quantum Uncertainty in Doubly Special Relativity
• De Sitter space as an arena for Doubly Special Relativity
• Six easy roads to the Planck scale
• de Sitter special relativity
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• Cosmological Term and Fundamental Physics
• Dual Kappa Poincare Algebra

Cited by in corpus (3)

• Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
• Dispersion relations in finite-boost DSR
• Geodesics, Mass and the Uncertainty Principle in a Warped de Sitter Space-time