Ebook: Symmetry

This book presents the geometric structure of the Higgs field, the geometry that is beyond the standard model based on a modification of the structure that appears in Escher´s Waterfall. The proposed structure is also a way to draw and visualize the since long time held idea that spacetime is quantized. It brings harmony between two colliding worlds in physics, general relativity and quantum mechanics.
There is a geometric representation of the quarks, the leptons and the four types of gauge bosons, the weak isospin and the geometry and algebra of many interactions and decays. The values of the Weinberg angle, the Cabibbo angle and the parameters of the CKM matrix are also given by the structure, as well as the geometry of special relativity, the tensors of general relativity, the measurement problem, the uncertainty principle, the second law of thermodynamics, neutrino oscillation and the PMNS matrix.
All the free parameters of the standard model find their precise values in the proposed structure. The fundamental constants -the gravitational constant, Boltzmann constant, Planck´s constant and the vacuum permittivity- are related by the golden ratio.
The second part is a description of the program that controls the perfectly symmetric distribution of the prime numbers among the natural numbers.
The third part connects the natural numbers and the primes with the structure described in the first part.