Lagrangian Mechanics of Massless Particles with Spin

Abstract

Lagrangian mechanics of massless particles with spin is studied, based on the interpretation that spin corresponds to displacement in complex directions. Starting with the action integral which ensures the masslessness of particles, two possibilities to introduce spin are investigated. In both cases, the equations of motion cannot fix the world line of massless spinning particles uniquely, due to a “gauge” invariance property of the action integral. The space-time coordinates are not the most suitable for describing massless spinning particles, but it is convenient to take a pair of spinor variables, i.e., a twistor, as the basic dynamical variables to which the canonical quantization procedure can be applied. In one of the two cases, where massless particles are considered to move in superspace with N spinor coordinates, it is found that massless particles form a spin (or helicity) multiplet with the helicity running from - N/4 to +N/4.