Which particles does the Fermi-Dirac function concern?

The Fermi-Dirac function specifically applies to particles that are identical and indistinguishable with half-integer spin, which are known as fermions. Fermions obey the Pauli exclusion principle, meaning that no two fermions can occupy the same quantum state simultaneously. This concept is crucial in describing the statistical distribution of particles like electrons, protons, and neutrons in systems at thermal equilibrium, particularly at low temperatures or in quantum systems.

In contrast to this, distinguishable particles or those with integer spin are described by different statistical distributions, namely Maxwell-Boltzmann for distinguishable particles and Bose-Einstein for bosons (which have integer spin). The nature of fermions and their statistical behavior makes the Fermi-Dirac function a vital tool in quantum mechanics and statistical physics, particularly in understanding the behavior of electrons in metals and the creation of phenomena such as superconductivity and the structure of white dwarfs.

Understanding these properties and their implications reinforces the significance of the Fermi-Dirac statistics in studying systems of fermions, distinguishing it from the behavior of bosons and other types of particles.