Quantum Field Theory (QFT) mandates anti-commutation relations for fermion fields to ensure a consistent quantum theory that precludes negative energy states in the Hamiltonian spectrum, unlike commutation relations which would imply catastrophic vacuum instability. This enforcement of Fermi-Dirac statistics is the rigorous physical manifestation of the Spin-Statistics Theorem, establishing an inseparable link between particle spin and algebraic behavior where half-integer spins must obey anti-commutators $\{a_i, a_j^\dagger\} = \delta_{ij}$ to satisfy causality via space-like anticommutativity. Consequently, relativistic single-particle descriptions derived from the Dirac equation are superseded by second quantization frameworks involving creation and annihilation operators acting on Fock states.
Quantum Field Theory (QFT) mandates anti-commutation relations for fermion fields to ensure a consistent quantum theory that precludes negative energy states in the Hamiltonian spectrum, unlike commu…