Two Dimensional Lattice Gauge Theory with and without Fermion Content

Authors

Dibakar Sigdel, FIUFollow

Document Type

Thesis

Degree

Doctor of Philosophy (PhD)

Major/Program

Physics

First Advisor's Name

Rajamani Narayanan

First Advisor's Committee Title

Major Professor

Second Advisor's Name

Misak M. Sargsian

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

H Rudolf Fiebig

Third Advisor's Committee Title

Comittee Member

Fourth Advisor's Name

Gueo Grantcharov

Fourth Advisor's Committee Title

Comittee Member

Keywords

Lattice QCD, Gauge theory, quarks and gluons, QCD in 2D, gauge fixing, fermions on the lattice, pure gauge theory

Date of Defense

11-3-2016

Abstract

Quantum Chromo Dynamics (QCD) is a relativistic field theory of a non-abelian gauge field coupled to several flavors of fermions. Two dimensional (one space and one time) QCD serves as an interesting toy model that shares several features with the four dimensional physically relevant theory. The main aim of the research is to study two dimensional QCD using the lattice regularization.

Two dimensional QCD without any fermion content is solved analytically using lattice regularization. Explicit expressions for the expectation values of Wilson loops and the correlation of two Polyakov loops oriented in two different directions are obtained. Physics of the QCD vacuum is explained using these results.

The Hamiltonian formalism of lattice QCD with fermion content serves as an approach to study quark excitations out of the vacuum. The formalism is first developed and techniques to numerically evaluate the spectrum of physical particles, namely, meson and baryons are described. The Hybrid Monte Carlo technique was used to numerically extract the lowest meson and baryon masses as a function of the quark masses. It is shown that neither the lowest meson mass nor the lowest baryon mass goes to zero as the quark mass is taken to zero. This numerically establishes the presence of a mass gap in two dimensional QCD.

Identifier

FIDC001748

ORCID

orcid.org/0000-0002-2599-1192

Recommended Citation

Sigdel, Dibakar, "Two Dimensional Lattice Gauge Theory with and without Fermion Content" (2016). FIU Electronic Theses and Dissertations. 3224.
https://digitalcommons.fiu.edu/etd/3224