We investigate whether retarded scalar propagators on causal sets can be expressed in terms of the link matrix $\mathbf{L}$. For Poisson sprinklings into $1+1$ dimensional Minkowski spacetime, we show by asymptotic analysis and supporting numerical simulations that the averaged massless retarded propagator is naturally associated with a normalized exponential $\exp (\mathbf{L})$. We then extend the construction to the massive case via the usual mass-scattering series and obtain good agreement with the continuum propagator after averaging. Finally, we discuss the inverse kernel $\exp (-\mathbf{L})$ as a possible candidate for a discrete d’Alembertian.

Close

PrevNext

View figure in article

• Classical solutions in field theory
• Spacetime topology & causal structure