Definitions

# Exchange force

In particle physics, an exchange force is a force produced by the exchange of force carrier particles, such as the electromagnetic force produced by the exchange of photons between electrons and the strong force produced by the exchange of gluons between quarks. The idea of an exchange force implies a continuous exchange of particles which accompany the interaction and transmit the force, a process that receives its operational justification through the Heisenberg uncertainty principle. These exchange forces are not the same as the exchange interaction, also sometimes called the exchange force, between electrons which arises from a combination of the identity of particles, exchange symmetry, and the electrostatic force.

## History

One of the earliest uses of the term interaction was in a discussion by Niels Bohr in 1913 of the interaction between the negative electron and the positive nucleus. Exchange forces were introduced by Werner Heisenberg (1932) and Ettore Majorana (1933) in order to account for the saturation of binding energy and of nuclear density. This was done in analogy to the quantum mechanical theory of covalent bonds, such as exist between two hydrogen atoms in the hydrogen molecule wherein the chemical force is attractive if the wave function is symmetric under exchange of coordinates of the electrons and is repulsive if the wave function is anti-symmetric in this respect.

## Overview

To illustrate the concept of exchange interaction, any two electrons, for example, in the universe are considered indistinguishable particles, and so according to quantum mechanics in 3 dimensions, every particle must behave as a boson or a fermion. In the former case, two (or more) particles can occupy the same quantum state and this results in a lack of exchange interaction between them; in the latter case, the particles can not occupy the same state according to the Pauli exclusion principle. From Quantum field theory, the spin-statistics theorem demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Thus, it so happens that all electrons are fermions, since they have spin 1/2.

As a mathematical consequence, fermions exhibit strong repulsion when their wave function overlap, but bosons do not. This repulsion is what the exchange interaction models. Fermi repulsion results in "stiffness" of fermions. That is why atomic matter, is "stiff" or "rigid" to touch. Where wave functions of electrons overlap, Pauli repulsion takes place. The same is true for protons and neutrons where due to their larger mass, the rigidity of baryons is much larger than that of electrons.