The discussion of any new topic necessarily makes use of knowledge that is to some extent assumed to have been already acquired. One cannot start from the very beginning and teach the whole of physics every time something new is to be introduced – even though the Landau and Lifshitz series of books comes close to pulling it off. More pragmatically, I would like to make sure that we are all on the proverbial same page with some of the basic notions. And where, you may ask, are these basic notions learned? I have in mind what can be called the canon of physics, that is, the books where we, as students, first studied the basic concepts and equations, the books that everyone has read to study, say, classical mechanics, electromagnetism, quantum mechanics, thermodynamics and statistical mechanics – as well as the mathematical tools necessary to comprehend the equations and the statistics to make sense of the data analysis. I have them (most of them, at least) in my office, and so do most of the physicists I know. The covers of some of them are shown in Figure 2.1.

This chapter is devoted to the topological and geometric structures of a causal fermion system.

We introduce solutions to the diffusion equation (Fick’s second law), which arises from Fick’s first law and continuity. Diffusion into semi-infinite half spaces as well as problems in finite spaces and the approach to equilibrium are addressed and solutions are given. The second part of the chapter describes fundamental, atomic scale aspects of diffusion in the solid state.

It is time to face the elephant in the room. Beautiful though they are, the gauge bosons of the weak interactions are massless and cannot be the mediators of the weak interactions. They do not reproduce Fermi’s interaction at low energy. They make the weak interactions long range while they are most definitely not.

The existence of minimizers is proven using measure-theoretic tools.

The powerful methods of dimensional analysis are introduced via the pi-theorem. The reader discovers that many of the results obtained in Chapters 3 and 4 can be arrived at using dimensional analysis alone. These include drag and pipe flow. Dynamical similarity is explained.

We define and explain the basic objects and structures of a causal fermion system.

We summarize some basics on quantum mechanics and relativity theory as needed in order to understand the physical content and context of the theory of causal fermion systems.

In this chapter we study the idealised, inviscid fluid. The central formula is Bernoulli’s equation, and its consequences are explored in a number of examples. Next we look at flow which is irrotational (vortex free) and develop potential theory, which in two dimensions can be treated very elegantly using complex analysis and the Cauchy–Riemann equations.

The initial-value problem for the linearized field equations is developed.

This chapter is mostly about solid mechanics: Cauchy stress, finite and infinitesimal strain, rotation. Velocity and acceleration are developed in both inertial and non-inertial fames. This is central to the education of the physicist and engineer, but the development leads to a derivation of the Navier–Stokes equations, which are central to fluid dynamics.