A No-go theorem for Poincar\'e-invariant networks

TL;DR

This paper proves that it is impossible to construct Poincaré-invariant networks with a locally finite distribution of nodes and links in Minkowski spacetime of any dimension, highlighting fundamental limitations in such network models.

Contribution

The paper establishes a no-go theorem demonstrating the impossibility of creating Poincaré-invariant networks with locally finite distributions in Minkowski spacetime.

Findings

No Poincaré-invariant networks with locally finite distributions exist in Minkowski spacetime.

The proof applies to any spacetime dimension.

Fundamental limitations are identified for network models respecting Poincaré symmetry.

Abstract

I explain why there are no Poincar\'e-invariant networks with a locally finite distribution of nodes and links in Minkowski-spacetime of any dimension.