Kappa-deformed Snyder spacetime

TL;DR

This paper introduces a new class of noncommutative spacetime models that interpolate between Snyder and kappa-Minkowski spaces, providing realizations, algebraic structures, and implications for deformed special relativity.

Contribution

It presents Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra, unifying Snyder and kappa-Minkowski models with new realizations and algebraic structures.

Findings

Realizations of noncommutative coordinates in terms of commutative ones.

Deformed Leibniz rule, coproduct, and star product structures.

Connection to deformed special relativity theories.

Abstract

We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.