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Quantum field theory on quantum graphs and application to their conductance

E Ragoucy

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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 that already proposed using the 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 literature. 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.


PACS

11.10.-z Field theory

02.10.Ox Combinatorics; graph theory

11.55.-m S-matrix theory; analytic structure of amplitudes

MSC

81U20 S-matrix theory, etc.

05C50 Graphs and matrices

81Txx Quantum field theory; related classical field theories (See also 70Sxx)

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 29 (24 July 2009)

Received 27 January 2009, in final form 2 June 2009

Published 30 June 2009



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