2005/12/31 by C. D. Fosco, J. Sánchez-Guillén, J. Sanchez-Guillen +2
Engineering · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Dirac (video compression format) #Effective action #Gauge (firearms) #Mathematical physics #Particle Accelerators and Free-Electron Lasers #Path integral formulation #Physics #Propagator #Pulsars and Gravitational Waves Research #Quantum mechanics #Spacetime #Spin (aerodynamics) #Theoretical physics #hep-th
paper · pdf · doi:10.1016/j.aop.2007.06.007
published as AnnalsPhys.323:356-372,2008 · 23 pages, no figures. Version extended with some applications and a more detailed explanation of the classical limit
arxiv created 2007/06/21 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We 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[x2(τ)- 1]. The second agrees exactly with the spin action one should expect for a spin-1/2 field.