Year: 2023

Quasicrystalline Spin Foam with Matter: Definitions and Examples

In this work, we define quasicrystalline spin networks as a subspace within the standard Hilbert space of loop quantum gravity, effectively constraining the states to coherent states that align with quasicrystal geometry structures. We introduce quasicrystalline spin foam amplitudes, a variation of the EPRL spin foam model, in which the internal spin labels are constrained […]

Three Fibonacci-chain aperiodic algebras

Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered structures and in the construction of some integrable models in quantum mechanics. Starting from the works of Patera and Twarock we present […]

SL(2, C) Scheme Processing of Singularities in Quantum Computing and Genetics

Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing like the fast Fourier transform, Ramanujan sum signal processing and many other techniques. For space-time topological objects in physics and biology, we propose a a type of algebraic processing based on schemes in which the discrimination […]