Fermionic Path Integrals

Fermionic path integrals are mathematical tools used in quantum physics to describe particles like electrons that follow Fermi-Dirac statistics. Instead of thinking about particles moving along specific paths, physicists sum over all possible configurations, incorporating their quantum properties. Fermions have unique behavior, such as obeying the Pauli exclusion principle, which states no two can occupy the same state simultaneously. To handle this mathematically, fermionic variables use special algebraic entities called Grassmann variables, which anti-commute. Fermionic path integrals thus provide a framework for understanding and calculating the behavior of fermionic particles within quantum field theory.