Conformal symmetry for relativistic point particles

Abstract

In this paper we consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study is done for the case of two-particles, with a particular attention to the symmetries of the problem. In fact, we show that this analysis could be extended to the case of higher spin symmetries. Always in the two particle case a formulation in terms of bilocal fields is proposed. For a system of $N$ particles we consider two possible scenarios: i) action invariant under any permutation of the $N$ particles. This case corresponds to completely democratic interactions with each particle interacting with all the others. The action depends on $N-1$ dimensionless coupling constants. ii) By putting the particles along a one-dimensional lattice (open or closed) with nearest neighbor interactions, one obtains a model with only two-body interactions depending on a single dimensionless coupling. This model can be easily extended to the continuum case, obtaining a conformal string-like (closed or open) system.

arXiv commentVersion accepted for publication in Phys. Rev. D

References in corpus (8)

• Gauge Theory Correlators from Non-Critical String Theory
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Introduction to the Classical Theory of Higher Spins
• Conformal Higher Spin Theory
• On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics
• Elements of Vasiliev theory
• Higher-Spin Theory and Space-Time Metamorphoses
• Killing tensors and canonical geometry

Cited by in corpus (7)

• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Null lifts and projective dynamics
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• A topological approach for emerging D-branes and its implications for gravity
• Conformal symmetry for relativistic point particles: an addendum
• A First-Quantized Model For Unparticles and Gauge Theories Around Conformal Window
• A classical mechanical model of two interacting massless particles in de Sitter space and its quantization