A classical mechanical model of two interacting massless particles in de Sitter space and its quantization

TL;DR

This paper extends a conformally invariant model of two massless particles from Minkowski to de Sitter space, analyzing its Hamiltonian structure and deriving a quantized wave equation that reduces to the Minkowski case in the limit.

Contribution

It generalizes a known conformally invariant particle model to de Sitter space and performs its Hamiltonian analysis and canonical quantization.

Findings

Derived a fourth-order differential wave equation for bilocal fields in de Sitter space.

Showed the wave equation reduces to the Minkowski space case as de Sitter radius approaches infinity.

Provided a Hamiltonian formulation consistent with Dirac's prescription for constrained systems.

Abstract

A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a way that the resulting, generalized action reduces to the original action in a limit that de Sitter radius goes to infinity. We analyze the Hamiltonian formulation in accordance with Dirac's prescription for constrained Hamiltonian systems and carry out its subsequent canonical quantization in coordinate representation following DeWitt. As the result, we derive a fourth-order differential wave equation for bilocal fields that, in the infinite radius limit, reproduces one obtained in the original model for Minkowski space case.