Finite propagation speed and causal free quantum fields on networks
arXiv:0907.1522 · doi:10.1088/1751-8113/42/49/495401
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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Cited by in corpus (11)
- Brownian Motions on Metric Graphs
- Non-equilibrium Steady States of Quantum Systems on Star Graphs
- Quantum Fields on Star Graphs with Bound States at the Vertex
- Particle creation and annihilation at interior boundaries: One-dimensional models
- Direct computation of scattering matrices for general quantum graphs
- Off-critical Luttinger Junctions
- The existence of the solution of the wave equation on graphs
- Multiscale methods for solving wave equations on spatial networks
- Zero modes of quantum graph Laplacians and an index theorem
- Many-particle quantum graphs: A review
- Emerging entanglement on network histories