Dual Kappa Poincare Algebra

TL;DR

This paper introduces a novel modification of the Poincare algebra called dual kappa Poincare algebra, which preserves Lorentz symmetry and alters how boosts affect spacetime and momenta, leading to a new phase space structure.

Contribution

It proposes a new dual kappa Poincare algebra that modifies spacetime and momentum transformations while maintaining Lorentz invariance, and derives its phase space algebra.

Findings

The dual kappa Poincare algebra preserves Lorentz algebra.

The phase space algebra is derived using the Heisenberg double construction.

Relations between dual kappa Poincare variables and special relativity variables are established.

Abstract

We show a different modification of Poincare algebra that also preserves Lorentz algebra. The change begins with how boosts affect spacetime in a way similar to how they affect the momenta in kappa Poincare algebra, hence the term "dual kappa Poincare algebra". Since by construction the new spacetime commutes, it follows that the momenta co-commute. Proposing a spacetime co-algebra that is similar to the coproduct in the bicrossproduct basis of kappa Poincare algebra, we derive the phase space algebra using the Heisenberg double construction. The phase space variables of the dual kappa Poincare algebra are then related to the SR phase space variables. From these relations, we complete the dual kappa Poincare algebra by deriving the action of rotations and boosts on the momenta.