Model of massless relativistic particle with continuous spin and its twistorial description

TL;DR

This paper introduces a new twistorial world-line model for massless particles with continuous spin, providing a novel twistor formulation and explicit space-time solutions for the associated fields.

Contribution

It develops a twistorial Lagrangian model for continuous spin particles and derives their space-time fields via a new twistor transform, advancing the theoretical understanding of such particles.

Findings

Constructed a new world-line Lagrangian for continuous spin particles.

Derived the twistor transform linking twistor and space-time fields.

Showed the space-time fields satisfy the irreducible Poincare group constraints.

Abstract

We propose a new world-line Lagrangian model of the D=4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After the first quantization of the world-line twistorial model, the wave function is defined by an unconstrained function on the two-dimensional complex affine plane. We find the twistor transform that determines the space-time field of the continuous spin particle through the corresponding twistor one, which plays the role of a prepotential. It is shown that this space-time field is an exact solution of the space-time constraints defining the irreducible massless representation of the Poincare group with continuous spin.