Radiative Effects in Low-Dimensional Effective Fermion Field Theory with Compactification

Abstract

The introduction of branes immersed in the space-times of higher dimensions revealed itself to be a useful instrument for the study of high-dimensional models in quantum field theory. Moreover, low-dimensional quantum field theories represent an especially interesting class of models in physics due to their unique properties and renormalizability when interactions are treated perturbatively. The advantages of both approaches can be combined in a model for a low-dimensional brane immersed in the usual tetradimensional Minkowski space-time, the properties of which are relatively well known. This approach can be used for the study of systems like graphene and carbon nanotubes. In the present work, we present an effective model for nanotubes based on the Lagrangian obtained from a tight-binding model for graphene. The induced current, appearing azimuthally in the presence of a magnetic flux through the tube section (Aharonov–Bohm effect), will be derived. A reduced Lagragian for photons confined on the tube surface, obtained from the literature, is included in the last part of the work to threat perturbative corrections to the induced current.