Finite propagation speed and causal free quantum fields on networks

Finite Propagation Speed and Causal Free Quantum Fields on Networks

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) ho...

On the Causal Propagation of Fields

By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary fields (such as scalar or electromagnetic ones). In particular, it provides a conservation theorem of the free gravitational field in all N -dimensional spacetime...

Quantum non-locality based on finite-speed causal influences leads to superluminal signalling

The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed1,2. Yet, any such experimental violation could always be explained in principle through models based on hidden influences propagating at a finite speed v > c, provided v is large enough3,4. Here, we sho...

Stability and Bifurcations in Neural Fields with Finite Propagation Speed and General Connectivity

A stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the propagation delays play a significant role in nonstationary bifurcations of equilibria, whereas the stationary...

On Completely Free Elements in Finite Fields