Finite propagation speed and causal free quantum fields on networks
Robert Schrader · Journal of Physics A Mathematical and Theoretical · 2009
Laplace operators on metric graphs give rise to Klein–Gordon and wave operators. Solutions of the Klein–Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then constructed, whose commutator function is just the Klein–Gordon kernel. As a consequence of finite propagation speed, Einstein causality (local commutativity) holds. Comparison is made with an alternative construction of free fields involving RT-algebras.