M.Sc. / Please refer to full text to view abstract

Fermion number fractionization in quantum field theory on a finite interval is studied for a (1 + 1) dimensional fermion-soliton system with explicit charge conjugation symmetry breaking. The effects of boundary conditions on the fractional fermion number and the connection with the corresponding open space problem are investigated. It is argued that the open space fractional charges can be correctly reproduced from the finite interval results only through a careful definition of what is meant by the soliton charge. This definition of the charge distinguishes between the fermionic and boundary induced charges in the system, and isolates the soliton from possibly other charged topological objects in the system. It therefore gives a true measure of the localized fractional fermion number induced on the soliton of interest. It is then rigorously proven that the corresponding charge fluctuations vanish, and hence that the induced fractional charge on the soliton is a quantum observable. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The anionic tridentate chelating ligands [MeGa(pz)₃]⁻, [MeGa(dmpz)₃]⁻, and [MeGa(mpz)₃]⁻ have been synthesized and their coordinative properties studied. The [MeGa(pz)₃]⁻ ligand acts as a six-electron chelating ligand to divalent transition metal ions giving complexes of the type [MeGa(pz)₃]₂M (M=Mn,Co,Ni,Cu,Zn), believed to possess an octahedral MN₆ core. The ligand also forms numerous carbonyl complexes with Mn, Mo and W. The tridentate chelating nature of this new ligand has been demonstrated through a crystal structure determination of the complex [MeGa(pz)₃]Mo(CO)₂(n³-C₃H₅). The [MeGa(dmpz)₃]⁻ ligand also forms carbonyl complexes of Mn, Mo and W. The ready conversion of this ligand to the less sterically demanding tris-chelating "hydroxy" ligand [MeGa(dmpz)₂(OH)]⁻ occurs in the attempted synthesis of "n³-allyl" complexes [MeGa(dmpz)₃]M(CO)₂ " n³-allyl" (where M=Mo or W, "n³-allyl"=n³-C₅H₅, n³-C₄H₇). The tridentate chelating nature of this "hydroxy" ligand is conclusively demonstrated in the crystal structure determination of the complex [MeGa(dmpz)₂(OH) ]Mo(C0)₂(n³-C₄H₇) . The [MeGa(mpz)₃]⁻ ligand forms transition metal complexes of the type [MeGa(mpz)₃]₂M (M=Co,Ni) and also carbonyl complexes of Mo and W. Less definitive results were obtained with this ligand, as characterization of the resulting complexes was complicated by the inability to separate the isomers possible for each complex The synthesis of the [H₂B(OCH₂CH₂NR₂)(pz)]⁻ (R=H, Me) ligands and their reaction with divalent transition metal ions is also described. In this case, the only products isolated were the previously characterized [H₂B(pz)₂]₂M and [HB(pz)₃]₂M (M=Co,Ni, Cu,Zn) complexes. Finally, details of the synthesis and characterization of the [R₂Ga(CH₃C0₂)] and [R₂Ga(C₄H₈NC0₂)] (R=Me,Et) compounds are given. The crystal structure of the [Me₂Ga(C₄H₈NC0₂)] derivative consisted of monomeric units linked to two others by weak Ga-0 bonds to form a chain-like polymeric structure. The gallium atom in this compound is five-coordinate and has distorted trigonal bipyramidal geometry. / Science, Faculty of / Chemistry, Department of / Graduate

Bibliography: pages 95-97. / A major obstacle to calculating Feynman diagrams in field theories, confined to a cavity, has always been the divergent loop diagrams. So far, only the quantum chromodynamic and electrodynamic self-energies of a ls1/2 quark, confined to a static spherical cavity, have been accurately calculated. These quantities are of immediate interest in the M.I.T. bag model. The existing methods to calculate loop diagrams are based on the multiple reflection scheme, in which the zero reflection term is separated out analytically, and evaluated separately. Thus far, there are some indications that this method is unsuitable for the quadratically divergent one loop vacuum polarization. In this thesis we firstly develop a set of Fourier transforms, appropriate to a discussion of renormalization in a cavity. Using these, we renormalize the cavity propagators to one loop for scalar, Dirac, and gauge fields. We then introduce a new computational method to subtract out the divergences, based on dimensional regularization. Using this method, we present results for various loop diagrams. The scalar φ⁴ theory is used as a pedagogical example. We then present the quark self-energy for several low lying cavity modes. Finally we tackle the long standing and hitherto unresolved question of the vacuum polarization. For this we give a detailed discussion of surface divergences, and present results for scalar quantum electrodynamics. We make a suggestion for the implementation of the running coupling constant in the cavity.

No description available.

No description available.

No description available.

That a theory is merely effective has historically counted against it, especially in pro-realism discourse. For example, many realists take the interpretation of a theory to amount to specifying what the world would be like was the theory true (or characterizing the possible worlds picked out by the theory). But effective theories are not true simpliciter. They describe a limited subset of nature and only approximately so, giving the traditional realist little to work with. The effective realist gives up on the traditional realist project, noting that contemporary physical theories tell us nothing, or very little, about what's fundamental. The traditional realist gives us unreliable results for our ontology at fundamental length scales. Effective realism responds by taking effective theories seriously. I have two primary goals in this paper. First, I consider a few responses to arguments provided by Ruetshce (2017). Ruetsche worries that the theory space over which the effective realist quantifies might fail to be comprehensive. I hope to defend the effective realist through the use of first-order scientific evidence and with a response motivated by Fraser (forthcoming). Second, I develop an objection to effective realism similar in kind to one posed by Ruetshce. Rather than a skepticism in the space on which the renormalization group acts, I entertain a more general skepticism with respect to the construction of effective field theories. I then tease out a response grounded in theory space constraints to justify the effective realist's use of effective field theories to guide ontological commitment. / Master of Arts / Realism, or the view that we can believe in the approximate truth of scientific theories or parts of those theories, has long struggled to overcome its skeptics. Many past theories have been discarded. Many new theories have replaced their predecessors. Many problems plague our interpretations of the results of the theories we have access to. To bolster the case for realism, I defend a modest view in the context of high energy physics by taking advantage of a tool called renormalization. The tool allows us to partly characterize domains that we have not yet empirically probed, and I argue that this provides fertile grounds for realism.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 5 June 2017. / The holographic computation of extremal correlators is often frustrated by divergences. The interpretation of these divergences is incomplete. The primary goal of this study is to develop a better understanding of these divergences. Towards this end, working within the AdS/CFT correspondence we review the computation of correlators. In the field theory we review well known matrix model techniques useful to study the planar limit, as well as methods exploiting group representation theory that are useful for the computation of correlators in large N but non-planar limits. On the gravity side of the correspondence, we describe in detail the computation of two- and three point functions of a scalar field coupled to gravity on the Euclidian AdSd+1 space, three-point functions of two giant gravitons and one pointlike graviton as well as correlators of Kaluza-Klein gravitons. A key observation of this study is that extremal correlators are mapped to scattering amplitudes of particles with parallel momenta. These are naturally accompanied by involve collinear divergences. Therefore, we suggest that the divergences in the computation of extremal correlators are linked to collinear divergences. A lot more work is needed to establish this connection. / LG2017

No description available.