Rigid particle revisited: Extrinsic curvature yields the Dirac equation

•New way of canonical quantization of relativistic rigid particle is proposed.•Quantization made in terms of so(3.2)so(3.2) angular momentum algebra.•Quantization yields massive Dirac equation.

We reexamine the model of relativistic particle with higher-derivative linear term 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)so(3.2)-algebra yields massive Dirac equation.