# Introduction to Mathematical Physics/N body problem and matter description/Introduction

As noted in the introduction to this book, ${\displaystyle N}$ body problem ([ph:physt:March95],[ph:physt:Mattuck92]) is the fundamental problem that spanned modern physics, sustaining reductionnist approach of Nature. The element considered depend on the scale chosen to describe the matter. Each field of physics has its favourite N body problem:

• nuclear physics deals with sets of nucleons.
• atomic physics deals with interactions between nucleus and nucleons.
• molecular chemistry, solid state physics, physics of liquids, gas, plasmas deals with interactions between atoms.
• classical mechanics and electrodynamics, ${\displaystyle N}$ body problems can arise (planet movement for instance).
• en astrophysics one studies interactions between stars, galaxies, and clusters of galaxies.

Once fundamental elements making matter are identified, the interaction between systems made of ${\displaystyle N}$ such fundamental elements should be described. Note that the interaction between constituents change with the lenght scale considered. Nuclear physics deals mostly with strong interaction (and weak interaction). Atomic physics and molecular physics deal mostly with electromagnetic interaction. Astrophysics deals with gravitation and ther other interactions[1]

This chapter is purely descriptive. No equations are presented. The subatomic systems will not be more treated in the next chapters. However, the various forms of matter that can be considered using, as elementary block, atomic nucleus and its electrons will be treated in the rest of the book. For each form of matter presented here, numerous references to other parts of the books are proposed. Especially, chapter N body problem in quantum mechanics, treats of quantum properties of eigenstates of such systems (the Schrödinger evolution equation is solved by the spectral method). Chapter N body problems and statistical equilibrium treats of their statistical properties.

1. Indeed, in the description of stars for instance, gravitational pressure implies that fusion reaction are possible and that all atoms are ionized, thus interacting via electromagnteic interaction