by Nga-Wai Liu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 161-166. / Chapter Chapter 0 --- Introduction / Chapter 0.1 --- Historical background I ´ؤ The Atiyah-Singer index theorem --- p.1 / Chapter 0.2 --- Historical background II ´ؤGauge theory --- p.3 / Chapter 0.3 --- Arrangement of the thesis --- p.5 / Chapter Chapter 1 --- Fredholm operators / Chapter 1.1 --- Basic propetries --- p.7 / Chapter 1.2 --- Compact operators --- p.8 / Chapter 1.3 --- Homotopy- invariance of the index --- p.9 / Chapter 1.4 --- Family of Fredholm operators ´ؤ Index bundle --- p.13 / Chapter 1.5 --- Wiener-Hopf operators --- p.19 / Chapter Chapter 2 --- K-theory / Chapter 2.1 --- K-theory of compact spaces --- p.24 / Chapter 2.2 --- K-theory with compact support --- p.28 / Chapter 2.3 --- Bott periodicity theorem --- p.32 / Chapter 2.4 --- Difference construction --- p.44 / Chapter 2.5 --- Thom isomorphism theorem on K-theory --- p.51 / Chapter Chapter 3 --- Operators on manifolds / Chapter 3.1 --- Differential operators on Euclidean spaces --- p.54 / Chapter 3.2 --- Differential operators on manifolds --- p.55 / Chapter 3.3 --- Pseudodifferential operators on Euclidean spaces --- p.58 / Chapter 3.4 --- Pseudodifferential operators on manifolds --- p.62 / Chapter 3.5 --- Elliptic operators --- p.70 / Chapter 3.6 --- Tensor products --- p.76 / Chapter Chapter 4 --- Atiyah-Singer index theorem / Chapter 4.1 --- The topological index --- p.84 / Chapter 4.2 --- The analytical index --- p.87 / Chapter 4.3 --- The Atiyah-Singer index theorem --- p.89 / Chapter 4.4 --- Characteristic classes --- p.95 / Chapter 4.5 --- Thorn isomorphisms --- p.98 / Chapter 4.6 --- Cohomological formulation of the topological index --- p.101 / Chapter Chapter 5 --- Geometric preliminaries / Chapter 5.1 --- "Connections on principal bundles, and associated bundles" --- p.104 / Chapter 5.2 --- Gauge transformations --- p.109 / Chapter 5.3 --- Riemannian geometry --- p.112 / Chapter 5.4 --- Bochner-Weitzenboch formula --- p.116 / Chapter 5.5 --- Characteristic classes via curvature forms --- p.121 / Chapter 5.6 --- Holonomy --- p.126 / Chapter Chapter 6 --- Gauge theory / Chapter 6.1 --- The Yang-Mills functionals --- p.128 / Chapter 6.2 --- Instantons on S4 --- p.131 / Chapter 6.3 --- Moduli of self-dual connections --- p.142 / Chapter 6.4 --- Manifold structure for Moduli of self-dual connections --- p.153 / References --- p.161

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Orientador: Bruto Max Pimentel Escobar / Mestre

Bibliography: leaves 124-127.

Bibliography: leaves 124-127. / ix, 127 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002

Bibliography: p. 222-229. / vii, 229 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Constructs an overlap operator to realise chiral symmetry on a quantum chromodynamic lattice that is faster to evaluate computationally than the Dirac operator, though the use of an alternative kernel, the Fat Link Irrelevant Clover (FLIC) action. Investigates the properties of FLIC Overlap fermions through the quark propagator in momentum space via topology. These calculations are performed in both the quenched and the dynamical kernel approximation, a type of partial quenching. In the quenched approximation, the effects of fermion vacuum fluctuations are neglected in the creation of gluon field configurations, In the partially quenched approximation, a different fermionic action is used in the sea and valence sectors. Develops a means of including the effects of FLIC sea fermions in the gluonic background field and presents an implementation of code optimised for cluster computing. / Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2004

No description available.

No description available.

We investigate the dynamical generation of fermion mass in quantum electrodynamics (QED). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and the photon propagator. First, we study dynamical fermion mass generation in quenched QED with the Curtis-Pennington vertex, which satisfies the Ward-Takahashi identity and moreover ensures the multiplicative renormalizability of the fermion propagator. We apply bifurcation analysis to determine the critical point for a general covariant gauge. In the second part of this work we investigate the dynamical generation of fermion mass in full, unquenched QED. We develop a numerical method to solve the system of three coupled non-linear equations for the dynamical fermion mass, the fermion wavefunction renormalization and the photon renormalization function. Much care is taken to ensure the high accuracy of the solutions. Moreover, we discuss in detail the proper numerical cancellation of the quadratic divergence in the vacuum polarization integral and the requirement of using smooth approximations to the solutions. To achieve this, we improve the numerical method by introducing the Chebyshev expansion method. We apply this method to the bare vertex approximation to unquenched QED to determine the critical coupling for a variety of approximations. This culminates in the detailed, highly accurate, solution of the Schwinger-Dyson equations for dynamical fermion mass generation in QED including both, the photon renormalization function and the fermion wavefunction renormalization in a consistent way, in the bare vertex approximation and, for the first time, using improved vertices. We introduce new improvements to the numerical method, to achieve the accuracy necessary to avoid unphysical quadratic divergences in the vacuum polarization with the Ball-Chiu vertex.

Title page, contents and abstract only. The complete thesis in print form is available from the University of Adelaide Library. / In this thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1284180 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2007