What Fermi-Dirac statistics describe — the distribution of fermions, which obey the exclusion principle

What the spin-statistics theorem connects — integer spin particles are bosons, half-integer spin are fermions

Spin-statistics theorem: Integer spin = bosons, half-integer spin = fermions

What the Pauli exclusion principle forbids — two identical fermions from occupying the same quantum state

Pauli exclusion principle prohibits two identical fermions from sharing the same quantum state simultaneously

Why the Dirac equation has negative energy solutions — interpreted as positrons, confirmed by Anderson in 1932

Dirac equation predicts negative energy states, later identified as antiparticles, positrons, by Anderson's experiments

What the Dirac equation predicted — relativistic quantum mechanics requires antimatter to exist

Dirac equation predicted the existence of antimatter in relativistic quantum mechanics

What the Boltzmann distribution describes — probability of a state with energy E is proportional to e^(-E/kT)

Boltzmann distribution: Probability of state E ∝ e^(-E/kT)

What a Cooper pair is — two electrons with opposite spin and momentum bound through lattice vibrations

Cooper pairs: bound electrons with opposite spins and momenta via phonon-mediated attraction in superconductors