Introduction

1. p-Adic physics and unification of real and p-adic physics

2. TGD and classical number fields

3. Infinite primes

4. p-Adic fusion and fusion of real and p-adic physics to a single coherent whole

p-Adic physics and the fusion of real and p-adic physics to a single coherent whole

1. Background

2. Summary of the basic physical ideas

3. p-Adic numbers

4. What is the correspondence between p-adic and real numbers?

5. p-Adic variants of the basic mathematical structures relevant to physics

6. Quantum physics in the intersection of p-adic and real worlds

TGD and classical number fields

1. Quaternion and octonion structures and their hyper counterparts

2. Quaternions, octonions, and modified Dirac equation

3. Number theoretical compactification and M⁸-H duality

Octo-twistors and twistor space

1. Two manners to twistorialize imbedding space

2. Octotwistorialization of M⁸

3. Octonionicity, SO(1,7), G₂, and non-associative Malcev group

4. Octonionic spinors in M⁸ and real complexified-quaternionic spinors in H?

5. What the replacement of SO(7,1) sigma matrices with octonionic sigma matrices could mean?

6. Could octonion-analyticity solve the field equations?

Infinite primes

1. Basic ideas

2. Infinite primes, integers, and rationals

3. Can one generalize the notion of infinite prime to the non-commutative and non-associative context?

4. How to interpret the infinite hierarchy of infinite primes?

5. How infinite primes could correspond to quantum states and space-time surfaces?