Bosonization in 1 + 1/2 dimensions

In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Fuentes, Manuel Alejandro

Contributors dc:contributor

• Fradkin, Eduardo H.

• Physics, Condensed Matter

Statement dc:rights

• Copyright 1995 Fuentes, Manuel Alejandro

Language dc:language

eng

Identifier

AAI9624347
(UMI)AAI9624347

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19406