  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.
