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

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.

Superfield continuous spin equations of motion

“…The last two are the additional supersymmetric constraints in order to describe sCSR. Equations (36,37) For the case of the chiral superfield description, eq (34,35,36,37) take the form 11 :…”

Twistorial and space-time descriptions of massless infinite spin (super)particles and fields

“…In [36,37] we propose that the twistorial formulation of the infinite (continuous) spin particle is described by the bosonic Weyl spinors π α ,πα := (π α ) * , ρ α ,ρα := (ρ α ) * ,…”

“…In our recent papers [36,37] we constructed a new model of an infinite (continuous) spin particle, which is a generalization of the twistor formulation of standard (with fixed helicity) massless particle [38,39,40] to massless infinite spin representations. As a result of a quantization procedure, we obtained infinite spin fields that demonstrate a transparent decomposition of continues spin irreducible representations into infinite sum of states with all helicities.…”

“…Besides, using the field twistor transform, we can now get the space-time-spinorial description of infinite spin fields with integer or half-integer helicities that form a supermultiplet of infinite spins [6,18]. This paper is based on the results obtained in [36,37].…”

Lagrangian formulation for the infinite spin N = 1 supermultiplets in d = 4

“…Infinite spin fields (see [1,2] and references therein) have attracted a lot of interest recently. A number of different approaches for their description were proposed [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Also the investigations of possible interactions for such fields started [23][24][25].…”