A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems

Abstract

One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum systems such as the particle in a box and the vibrational frequencies of diatomic molecules, such as hydrogen. The results shown here open a suggestive pathway for the use of graph-theoretical approaches in predicting properties of elementary particles and other physical systems, which seem to match similar topological patterns.

Molecular Topology Applied to the Discovery of 1-Benzyl-2-(3-fluorophenyl)-4-hydroxy-3-(3-phenylpropanoyl)-2H-pyrrole-5-one as a Non-Ligand-Binding-Pocket Antiandrogen

“…Topological indices (TIs) are “numbers that characterize a specific aspect of a molecule” . One of the advantages of MT is the fast and accurate prediction of many physicochemical − and biological − properties. Furthermore, topological descriptors have been applied to predict potential side effects of drug candidates, , and several patents have been derived from the application of MT as a computer-aided drug design (CADD) approach. − …”

A Graph Theoretical Interpretation of Different Types of Energies of Elementary Particles, Atoms and Molecules

“…In an article published by the author a few years ago [1], it was proved that the masses of the 12 elementary particles of the standard model (fermions) and the vibrational energies of the hydrogen molecule can be accurately predicted using the same approach. Specifically, the formalism consisted of assigning graphs with increasing number of loops to the increasing energy levels, following the same pattern as the classical stationary waves.…”