Computer Science – Numerical Analysis
Scientific paper
Oct 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009phdt........75j&link_type=abstract
ProQuest Dissertations And Theses; Thesis (Ph.D.)--The University of Western Ontario (Canada), 2009.; Publication Number: AATNR5
Computer Science
Numerical Analysis
Scientific paper
In chapter 1, we give an introduction to this thesis. Through this introduction, we present a literature review on the three topics, the vector condensation and its applications, the derivative expansion and renormalization group equation, and the neutrino in cosmology, that are studied in this thesis. In chapters 2 and 3, we study the gluonic condensation in non-Abelian gauge field theories at finite density of a scalar field. For scalars in the fundamental representation, there exists a stable global vacuum, with both rotational symmetry and electromagnetic U(1)em being spontaneously broken. We can also identify metastable vacua with an abnormal number of Nambu-Goldstone bosons in this theory. The SO(2) symmetry of these vacua corresponds to locking the gauge, flavor and spin degrees of freedom. If gluon condensation occurs in a phase of cold quark matter, we call this phase the gluonic phase. In chapter 4, a numerical analysis for the Meissner mass in the simplest gluonic phase is performed in the framework of the gauged Nambu-Jona-Lasinio model with two flavors. It is revealed that the gapless mode yields a characteristic contribution to the Meissner mass. We find that the simplest gluonic phase resolves the chromomagnetic instability in a rather wide region of the coupling constant. In chapter 5, we describe vortex solutions in the gauged SU(2)C x U(1)Y sigma model with a chemical potential for the hypercharge Y. It is shown that there are three types of topologically stable vortices in the model, connected either with photon field or the hypercharge gauge field, or with both of them. Explicit vortex solutions are numerically found and their energy per unit length is calculated. In chapter 6, the gauge theory at finite density in a spherically symmetric curved spacetime is studied. Both regular solutions and black hole solutions at zero density are found. It is revealed that the nonzero chemical potential will destroy the existence of black hole solutions in this model. In chapter 7, we study the term in the derivative expansion of effective action in scalar electrodynamics that is second order in the derivatives of the external field and all orders in a constant external field. It is found that this "kinetic term" for the scalar field could be expressed entirely in terms of the renormalization group functions. These renormalization group functions can be related to those associated with minimal subtraction. The results here are directly generalizable to the Standard Model with a Higgs with zero bare mass. In chapter 8, we propose using the cosmic neutrino background as a test of the Copernican principle. It is shown that from the theoretical perspective, the cosmic neutrino background can allow one to determine whether the Copernican principle is valid or not, but to implement such an observation, larger neutrino detectors are called for. Keywords: gauge theory, vector condensation, gluonic condensation, Nambu-Jona-Lasinio model, 2SC phase, cold quark matter, QCD matter, vortex solution, spherically symmetric solutions, black hole solutions, Einstein-Yang-Mills-Higgs theory, derivative expansion, Higgs mass, effective potential, Copernican principle, cosmic neutrino background.
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