Quantum Field Theory on Star Graphs

Abstract

We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex operators, we solve the model exactly for scale invariant boundary conditions, formulated in terms of the fermion current and without dissipation. The critical points are classified and determined explicitly. These results are applied for deriving the charge and spin transport, which have interesting physical features.

Talk presented at the Isaac Newton Institute programme Analysis on Graphs and its Applications (Cambridge 2007) -- to be published in Proceedings of Symposia in Pure Mathematics (AMS). LaTex 24+1 pages, 4 figures

References in corpus (3)

• Bosonization and Scale Invariance on Quantum Wires
• Quantum Fields on Star Graphs
• The inverse scattering problem for metric graphs and the traveling salesman problem

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• Unbalanced Holographic Superconductors and Spintronics
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• Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires
• Quantum Fields on Star Graphs with Bound States at the Vertex
• Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
• Particle creation and annihilation at interior boundaries: One-dimensional models
• Integrable Defects at Junctions within a Network
• A model with generalized Y-junction
• Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold