Exchange Interaction and Quantum State Symmetry
As another, entirely distinct, meaning of exchange force, it is sometimes used as a synonym for the exchange interaction, between electrons which arises from a combination of the identity of particles, exchange symmetry, and the electrostatic force.
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 functions 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.
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