Finite speed of propagation and local boundary conditions for wave equations with point interactions

TL;DR

This paper establishes a precise link between local boundary conditions in wave equations with point interactions and the finite speed of propagation of solutions, highlighting the importance of locality for physical realism.

Contribution

It proves that boundary conditions are local if and only if the wave equation exhibits finite speed of propagation, clarifying the relationship between boundary locality and wave dynamics.

Findings

Boundary conditions are local iff the wave equation has finite speed.

Finite speed of propagation is characterized by local boundary conditions.

The result connects mathematical boundary conditions with physical wave behavior.

Abstract

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation