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
Author(s): Gracia Arredondo
Edition: 1
Publisher: Gracia Arredondo
Year: 2019
Language: English
Pages: 216
City: Granada, Spain
Tags: Particle physics, mathematics, Symmetry, prime numbers
First part: Geometry beyond the standard model: Escher´s Waterfall 13
I. The geometry of the elementary particles 13
1. Introduction [1-11] 13
2. Matrix representation 19
3. Antimatter 21
4. Weak isospin 23
5. Conservation of angular momentum 25
6. Symmetry [15, 16] 25
7. The gauge bosons 26
8. Examples of decays and interactions [6, 7, 8, 9, 10, 11, 17, 18, 19] 30
9. The Weinberg angle, θw 95
10. The Cabibbo angle, θc 96
11. The CKM matrix 97
11. The angles of the three generations 101
II. Geometry of relativity and of some other questions in physics [23-36] 103
1. CPT. Duality of the structure 103
2. Intrinsic parity 106
3. The arrow of time: 106
4. Linking basic units. Velocity 108
5. Frame time and proper time in different inertial frames 111
6. The relativity of simultaneity 112
7. Energy, momentum and mass [38-41] 113
8. The mass of the fermions 118
9. Dark matter and dark energy 121
10. The cosmological constant [42] 122
11. The flatness problem [43] 122
12. Energy levels and the primes 124
13. Lorentz transformations [23] 125
14. Momenergy [23] 126
15. Parametric equations 127
16. Tidal forces 129
17. The stress-energy tensor 130
18. The Weyl tensor 138
19. Gravity and entropy gradients 140
20. The Ricci tensor 141
21. Neighbouring units: Gravity in action 142
22. What happens behind the scenes 143
23. The 8G factor. Spherical objects 145
24. Spherical object collapsing to form a black hole [46] 149
25. Geometric interpretation of the uncertainty principle 151
28. Geometry of the measurement problem 155
29. The infrared cut-off and the ultraviolet cut-off 157
30. Temperature and the Boltzmann constant 159
31. The second law of thermodynamics [32, 47] 160
32. Neutrino oscillation and the PMNS matrix 161
33. The vacuum expectation value, the coupling constants, the mass of the top 165
34. The interactions and the golden ratio 171
35. The hidden transactions within the golden ratio 172
36. The gate 173
37. A possible geometric representation of the space axes for other universes 174
38. Range of the interactions 175
39. Table with the main values obtained from the structure 177
40. The naturalness problem 179
Second part: The symmetry of the prime numbers 183
1. The program of the primes 183
2. The twin primes 194
3. Chained symmetries for the even numbers 196
4. Program of the odd composite numbers 197
Third part: The prime numbers in the structure 201
1. The natural numbers and the energy levels. The primes 202
2. The Goldbach´s conjecture and particle physics 204
3. The primes and the Riemann curvature tensor 209
