### Theoretical Calculations of the Masses of the Elementary Fermions [chapter]

Nathalie Olivi-Tran
2020 Accelerators and Colliders [Working Title]
Our universe is three-dimensional and curved (with a positive curvature) and thus may be embedded in a four-dimensional Euclidean space with coordinates x, y, z, t where the fourth dimension time t is treated as a regular dimension. One can set in this spacetime a four-dimensional underlying array of small hypercubes of one Planck length edge. With this array all elementary particles can be classified following that they are two-, three-, or four-dimensional. The elementary wavefunctions of
more » ... underlying array are equal to ffiffi ffi 2 p exp ix i ðÞ for x i ¼ x, y, z or to ffiffi ffi 2 p exp it ðÞ for t. Hence, the masses of the fermions of the first family are equal to 2 n (in eV/c 2 ) where n is an integer. The other families of fermions are excited states of the fermions of the first family and thus have masses equal to 2 n : p 2 ðÞ /2 where n and p are two integers. Theoretical and experimental masses fit within 10%.