Finite propagation speed and causal free quantum fields on networks
Robert Schrader
TL;DR
This paper investigates finite propagation speed in quantum fields on networks, establishing causality and constructing free quantum fields with specific commutator functions, comparing different approaches.
Contribution
It demonstrates finite propagation speed for Klein-Gordon and wave equations on metric graphs and constructs free quantum fields satisfying Einstein causality.
Findings
Finite propagation speed is proven for solutions on metric graphs.
Free quantum fields with Klein-Gordon kernel are constructed.
Causality is confirmed through local commutativity.
Abstract
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.
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