Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-01-16
J.Phys.A42:295205,2009
Physics
High Energy Physics
High Energy Physics - Theory
32 pages; misprints in tree graph corrected; proofs of consistency and unitarity added
Scientific paper
10.1088/1751-8113/42/29/295205
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter physics litterature. Then, we apply the construction for the calculation of the conductance of graphs, within a small distance approximation. The consistency of the approximation is proved by direct comparison with the exact calculation for the `tadpole' graph.
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