Elementary particles with continuous spin

TL;DR

This paper reviews the theoretical framework and recent developments concerning elementary particles with continuous spin, focusing on their group-theoretical descriptions and open issues for their physical relevance.

Contribution

It provides a comprehensive review of the group-theoretical and field-theoretical descriptions of continuous spin particles and discusses open problems in understanding their physical significance.

Findings

Continuous spin particles are described by unitary irreducible representations with infinite degrees of freedom.

The paper details the group-theoretical and field-theoretical frameworks for these particles.

Open issues remain crucial for determining their physical relevance.

Abstract

Classical results and recent developments on the theoretical description of elementary particles with "continuous" spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group (either Poincar\'e or anti de Sitter group) with an infinite number of physical degrees of freedom per spacetime point. Their basic group-theoretical and field-theoretical descriptions are reviewed in some details. We mention a list of open issues which are crucial to address for assessing their physical status and potential relevance.