Infinite spin particles

TL;DR

This paper explores the classical and quantum properties of infinite spin particles, revealing their unconventional features, interaction limitations, and the structure of their wave functions containing arbitrarily large spins.

Contribution

It introduces a higher order geometrical Lagrangian description for infinite spin particles and analyzes their interaction and quantization, including a superversion for half-odd integer spins.

Findings

Infinite spin particles are described by a reparametrization invariant higher order Lagrangian.

The model exhibits tachyonic behavior and light-like acceleration momenta.

Quantized wave functions contain arbitrary large spins.

Abstract

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to light-like accelerations. A simple higher order superversion for half-odd integer particles is also derived. Interaction with external vector fields and curved spacetimes are analyzed with negative results except for (anti)de Sitter spacetimes. We quantize the free theories covariantly and show that the resulting wave functions are fields containing arbitrary large spins. Closely related infinite spin particle models are also analyzed.