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.

Casalbuoni 和 Gomis [1] 提出了 Minkowski 空间中两个相互作用的无质量粒子的共形不变模型。我们从测地距离的角度将此模型推广到 de Sitter 空间的情况，以这样的方式，在 de Sitter 半径变为无穷大的限制下，由此产生的广义动作减少到原始动作。我们根据狄拉克对约束哈密顿系统的规定分析哈密顿公式，并在德威特之后在坐标表示中执行其随后的规范量化。结果，我们推导出了双局域场的四阶微分波动方程，该方程在无限半径极限内重现了在 Minkowski 空间情况下的原始模型中获得的方程。