Spin in the Worldline Path Integral in 2+1 Dimensions

Details Spin in the Worldline Path Integral in 2+1 Dimensions Spin in the Worldline Path Integral in 2+1 Dimensions

2005-12-07

arxiv.org/abs/hep-th/0512081v2

AnnalsPhys.323:356-372,2008

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.aop.2007.06.007

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 $x(\tau)$, the spacetime paths. We show that that action is a combination of a kinetic term plus a spin action. The first is proportional to $\delta[\dot{x}^2(\tau)- 1]$. The second agrees exactly with the spin action one should expect for a spin-1/2 field.

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