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arxiv: hep-th/0512081 · v2 · submitted 2005-12-07 · ✦ hep-th

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Spin in the Worldline Path Integral in 2+1 Dimensions

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classification ✦ hep-th
keywords actionfieldspinworldlinedimensionsgaugeintegralpath
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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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