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

I L Buchbinder,A Rusnak,A P Isaev,S Fedoruk

doi:10.1007/jhep07(2018)031

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 Poincaré group with continuous spin.

Highlights

JHEP07(2018)031 variables ym are intended to describe the spin degrees of freedom of massless particles
We propose a new world-line Lagrangian model of the D= 4 massless relativistic particle with continuous spin and develop its twistorial formulation
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

Summary

Space-time formulation

We begin with the construction of the new Lagrangian system for the relativistic particle corresponding to the Wigner-Bargmann space-time formulation of the irreducible continuous spin massless representation. In this approach equations (1.1)–(1.4) will arise as result of quantization of the particle model. Due to the constraints (2.3)–(2.6) the square of the Pauli-Lubanski pseudovector As result of this and (2.10), we see that the model (2.1) describes the massless particle with continuous spin. We note that the constraints (2.3)–(2.6) are suitable for the description of continuous spin particles in the Minkowski space-time of arbitrary dimension D= d+1 (see the review [23]). We will check the fulfillment of the condition (2.13) in constructing a new twistorial formulation of the continuous spin particle

Twistorial formulation of continuous spin particle

Quantization of twistorial model and continuous spin twistor field

Twistor transform for fields of continuous spin particles

Summary and outlook