Generalized relativistic kinematics in Poincaré-invariant models

Abstract

Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincaré invariance that preserves the Poincaré algebra, and only modifies its action on phase space in a Lorentz-invariant way. We show that, in contrast to the case where the Poincaré algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We give some nontrivial examples of this arising from doubly special relativity and noncommutative geometry and show that Hopf-algebra methods give equivalent results.

15 pages, plain TeX, some errors have been corrected

References in corpus (5)

• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• Scalar field theory in Snyder space-time: alternatives
• Relativistic kinematics beyond Special Relativity
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• The Area Quantum and Snyder Space

Cited by in corpus (7)

• Quantum field theory in generalised Snyder spaces
• Beyond Special Relativity at second order
• Lorentz invariant mass and length scales
• Dispersion relations in finite-boost DSR
• Relative-locality phenomenology on Snyder spacetime
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Relative-locality geometry for the Snyder model