Quantum Fields on Star Graphs with Bound States at the Vertex

Understand

We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires.

• The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix.
• The general case of off-critical scattering matrix with bound and/or antibound states is considered.
• We demonstrate that the contribution of these states to the scalar field is fixed by causality (local commutativity), which is the key point of our investigation.