Rigid particle revisited: extrinsic curvature yields the Dirac equation

TL;DR

This paper revisits the relativistic particle model with extrinsic curvature, demonstrating that its quantization leads to the Dirac equation, challenging previous assumptions about the model's properties.

Contribution

It shows that quantizing the rigid particle model with extrinsic curvature produces the Dirac equation, providing new insights into the model's quantum behavior.

Findings

Quantization yields the massive Dirac equation.

Contradicts common beliefs about the model's properties.

Uses $so(3.2)$-algebra in quantization process.

Abstract

We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of $so(3.2)$-algebra yields massive Dirac equation.