Research during the last decade demonstrates that effects originating on the Planck scale
are currently being tested in multiple observational contexts. In this review we discuss …

We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry
underlying the Snyder geometry is deformed at the co-algebraic level only, while its …

Long time ago, Yang [Phys. Rev. 72, 874 (1947)] proposed a model of noncommutative
spacetime that generalized the Snyder model to a curved background. In this paper, we …

In this work we discuss the deformed relativistic wave equations, namely the Klein–Gordon
and Dirac equations in a doubly special relativity scenario. We employ what we call a …

A bstract We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT
or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation …

The Yang algebra was proposed a long time ago as a generalization of the Snyder algebra
to the case of curved background spacetime. It includes as subalgebras both the Snyder and …

We review deformed quantum phase spaces and their realizations in terms of undeformed
phase space. In particular, methods of calculation for the star product, coproduct of momenta …

We describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on
three parameters β, κ and λ, which in a suitable algebra basis are described by the de Sitter …

We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting
cases, can be rigorously constructed through the projective geometry description of …

The star product usually associated with the Snyder model of noncommutative geometry is
nonassociative, and this property prevents the construction of a proper Hopf algebra. It is …