English

Spin in the Worldline Path Integral in 2+1 Dimensions

High Energy Physics - Theory 2008-11-26 v2

Abstract

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)x(\tau), 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[x˙2(τ)1]\delta[\dot{x}^2(\tau)- 1]. The second agrees exactly with the spin action one should expect for a spin-1/2 field.

Keywords

Cite

@article{arxiv.hep-th/0512081,
  title  = {Spin in the Worldline Path Integral in 2+1 Dimensions},
  author = {C. D. Fosco and J. Sanchez-Guillen and R. A. Vazquez},
  journal= {arXiv preprint arXiv:hep-th/0512081},
  year   = {2008}
}

Comments

23 pages, no figures. Version extended with some applications and a more detailed explanation of the classical limit

R2 v1 2026-07-22T15:33:29.972Z