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: 230
City: Granada
Tags: Symmetry, prime numbers, Beyond the standard model, Goldbach conjecture, CKM matrix, neutrino oscillations, Weinberg angle, Higgs field, Higgs boson
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
12. Mass of hadrons and leptons (in MeV) 102
II. Geometry of relativity and of some other questions in physics [23-36] 105
1. CPT. Duality of the structure 105
2. Intrinsic parity 109
3. The arrow of time 109
4. Linking basic units. Velocity 111
5. Frame time and proper time in different inertial frames 114
6. The relativity of simultaneity 115
7. Energy, momentum and mass [38-41] 116
8. The mass of the fermions 121
9. Dark matter and dark energy 124
10. The cosmological constant [42] 125
11. The flatness problem [43] 125
12. The wave function 127
13. Energy levels and the primes 128
14. Lorentz transformations [23] 129
15. Momenergy [23] 130
16. Parametric equations 131
17. Tidal forces 133
18. The stress-energy tensor 134
19. The Weyl tensor 142
20. Gravity and entropy gradients 144
21. The Ricci tensor 145
22. Neighbouring units: Gravity in action 146
23. What happens behind the scenes 148
24. The 8G factor. Spherical objects 150
25. Spherical object collapsing to form a black hole [46] 154
26. Geometric interpretation of the uncertainty principle and Planck´s constant 156
27. Geometry of the measurement problem and Planck´s constant 159
28. Temperature and Boltzmann constant 161
29. The infrared cut-off and the ultraviolet cut-off 162
30. The second law of thermodynamics [32, 47] 164
31. Neutrino oscillation and the PMNS matrix 165
32. The vacuum expectation value, the coupling constants, the mass of the top 169
33. The interactions and the golden ratio 175
34. The hidden transactions within the golden ratio 176
35. Range of the interactions 177
36. Table with the main values obtained from the structure 179
37. The naturalness problem 181
Second part: The symmetry of the prime numbers 187
1. The program of the primes 187
2. The twin primes 198
3. Chained symmetries for the even numbers 200
4. Program of the odd composite numbers 201
Third part: The prime numbers in the structure 205
1. The natural numbers and the energy levels. The primes 206
2. The Goldbach´s conjecture and particle physics 208
3. The primes and the Riemann curvature tensor 213
Fourth part: The process of thought 217
1. Thought as the CP conjugate of reality 217
References 223
