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