2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196115We construct a worldline path integral for the effective action and propagator of a Dirac field in 2+1 dimensions in an Abelian gauge field background. Integrating over an auxiliary gauge group variable we derive a worldline action depending only on $x(τ)$, the spacetime paths. We show that that action is a combination of a kinetic term plus a spin action. The first is proportional to $δ[\dot{x}^2(τ)- 1]$. The second agrees exactly with the spin action one should expect for a spin-1/2 field.23 pages, no figures. Version extended with some applications and a more detailed explanation of the classical limitHigh Energy Physics - Theorytext