No description available.

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 254-261).

No description available.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014 / Matrix models, and their associated integrals, are encoded with a rich structure, especially when studied in the large N limit. In our project we study the dynamics of a Gaussian ensemble of m complex matrices or 2m hermitian matrices for d = 0 and d = 1 systems. We rst investigate the two hermitian matrix model parameterized in \matrix valued polar coordinates", and study the integral and the quantum mechanics of this system. In the Hamiltonian picture, the full Laplacian is derived, and in the process, the radial part of the Jacobian is identi ed. Loop variables which depend only on the eigenvalues of the radial matrix turn out to form a closed subsector of the theory. Using collective eld theory methods and a density description, this Jacobian is independently veri ed. For potentials that depend only on the eigenvalues of the radial matrix, the system is shown to be equivalent to a system of non-interacting (2+1)-dimensional \radial fermions" in a harmonic potential. The matrix integral of the single complex matrix system, (d = 0 system), is studied in the large N semi-classical approximation. The solutions of the stationary condition are investigated on the complex plane, and the eigenvalue density function is obtained for both the single and symmetrically extended intervals of the complex plane. The single complex matrix model is then generalized to a Gaussian ensemble of m complex matrices or 2m hermitian matrices. Similarly, for this generalized ensemble of matrices, we study both the integral of the system and the Hamiltonian of the system. A closed sector of the system is again identi ed consisting of loop variables that only depend on the eigenvalues of a matrix that has a natural interpretation as that of a radial matrix. This closed subsector possess an enhanced U(N)m+1 symmetry. Using the Schwinger-Dyson equations which close on this radial sector we derive the Jacobian of the change of variables to this radial sector. The integral of the system of m complex matrices is evaluated in the large N semi-classical approximation in a density description, where we observe the emergence of a new logarithmic term when m 2. The solutions of the stationary condition of the system are investigated on the complex plane, and the eigenvalue density functions for m 2 are obtained in the large N limit. The \fermionic description" of the Gaussian ensemble of m complex matrices in radially invariant potentials is developed resulting in a sum of non-interacting Hamiltonians in (2m + 1)-dimensions with an induced singular term, that acts on radially anti-symmetric wavefunctions. In the last chapter of our work, the Hamiltonian of the system of m complex matrices is formulated in the collective eld theory formalism. In this density description we will study the large N background and obtain the eigenvalue density function.

Thesis (M.S.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on September 22, 2008) Includes bibliographical references.

No description available.

No description available.

Thesis (Ph. D.)--Oregon State University, 1971. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (M.S.) University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 27, 2007) Includes bibliographical references.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 136-144). Also available in electronic version.