## Space, Matter and Interactions in a Quantum Early Universe. Part I : Kac-Moody and Borcherds Algebras

We introduce a quantum model for the Universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac-Moody Lie algebra e9. We investigate Kac-Moody and Borcherds algebras, and we propose a generalization that meets further […]

## Space, Matter and Interactions in a Quantum Early Universe. Part II : Superalgebras and Vertex Algebras

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra 𝔤𝗎 that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn 𝔤𝗎 into a Lie superalgebra 𝔰𝔤𝗎 with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on 𝔰𝔤𝗎, […]

## Complete Quantum Information in the DNA Genetic Code

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature $G=\mathbb{Z}_5 \rtimes H$ where $H=\mathbb{Z}_2 . S_4\cong 2O$ is isomorphic to the binary octahedral group $2O$ and $S_4$ is the symmetric group on four letters/bases. […]

## Informationally complete characters for quark and lepton mixings

A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters κ of a finite group G. Here we introduce a d-dimensional Hilbert space with d=cc(G), the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two- […]

## Aspects of aperiodicity and randomness in theoretical physics

In this work we explore how the heat kernel, which gives the solution to the diffusion equation and the Brownian motion, would change when we introduce quasiperiodicity in the scenario. We also study the random walk in the Fibonacci sequence. We discuss how these ideas would change the discrete approaches to quantum gravity and the […]

## Symmetry transformation in Pd quasicrystals upon heating and hydrogenation

In this work, the structural transformation from a crystalline to quasicrystalline symmetry in palladium (Pd) and palladium-hydrogen (Pd-H) atomic clusters upon thermal annealing and hydrogenation has been addressed by means of atomistic simulations. A structural analysis of the clusters was performed during the heating up to the melting point to identify the temperature for the […]

## Synthesis of hydrogen storage materials in a Ti-Zr-Ni system using the hydride cycle technology during dehydrogenation by an electron beam in a vacuum

The synthesis of intermetallic material was carried out by means of dehydrogenating annealing of a (TiH 2) 30 Zr 45 Ni 25 sample in vacuum by an electron beam. The properties of the obtained material were studied for establishing the structural phase composition by scanning electron microscopy and X-ray structural analysis. It was found that […]

## Quantum computation and measurements from an exotic space-time R4

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state $||ψ⟩$ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite ‘contextual’ geometry. In […]

## The Self–Simulation Hypothesis Interpretation of Quantum Mechanics

We modify the simulation hypothesis to a self–simulation hypothesis, where the physical universe, as a strange loop, is a mental self–simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle of efficient language axiom. This leads to ontological interpretations about quantum mechanics. We […]