Quantum Field Theory on Star Graphs

TL;DR

This paper explores quantum field theory on star graphs, focusing on boundary conditions, symmetries, and scale invariance, and provides exact solutions for a four-fermion interaction model with applications to charge and spin transport.

Contribution

It offers an exact solution for a scale-invariant four-fermion interaction on star graphs using bosonization, classifies critical points, and analyzes transport properties.

Findings

Exact solutions for scale-invariant boundary conditions.

Classification and explicit determination of critical points.

Insights into charge and spin transport phenomena.

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.