On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Medication incident reporting in residential aged care facilities: Limitations and risks to residents' safety

Background Medication incident reporting (MIR) is a key safety critical care process in residential aged care facilities (RACFs). Retrospective studies of medication incident reports in aged care have identified the inability of existing MIR processes to generate information that can be used to enhance residents’ safety. However, there is little existing research that investigates the limitations of the existing information exchange process that underpins MIR, despite the considerable resources that RACFs’ devote to the MIR process. The aim of this study was to undertake an in-depth exploration of the information exchange process involved in MIR and identify factors that inhibit the collection of meaningful information in RACFs. Methods The study was undertaken in three RACFs (part of a large non-profit organisation) in NSW, Australia. A total of 23 semi-structured interviews and 62 hours of observation sessions were conducted between May to July 2011. The qualitative data was iteratively analysed using a grounded theory approach. Results The findings highlight significant gaps in the design of the MIR artefacts as well as information exchange issues in MIR process execution. Study results emphasized the need to: a) design MIR artefacts that facilitate identification of the root causes of medication incidents, b) integrate the MIR process within existing information systems to overcome key gaps in information exchange execution, and c) support exchange of information that can facilitate a multi-disciplinary approach to medication incident management in RACFs. Conclusions This study highlights the advantages of viewing MIR process holistically rather than as segregated tasks, as a means to identify gaps in information exchange that need to be addressed in practice to improve safety critical processes.

Moving from evaluation to trial: How do SMEs start adopting Cloud ERP?

The advent of cloud technology involving low subscription overheads cost has provided small and medium-sized enterprises (SMEs) with the opportunity to adopt new cloud-based corporate-wide systems (i.e., cloud ERP). This technology, operating through subscription-based services, has now provided SMEs with a complete range of IT applications that were once restricted to larger organisations. As anecdotal evidences suggest, SMEs are increasingly adopting cloud-based ERP software. The selection of an ERP is a complex process involving multiple stages and stakeholders, suggesting the importance of closer examination of cloud ERP adoption in SMEs. Yet, prior studies have predominantly treated technology adoption as a single activity and largely ignored the issue of ERP adoption in SMEs. Understanding of the process nature of the adoption and the factors that are important in each stage of the adoption potentially may result in guiding SMEs to make well-informed decisions throughout the ERP selection process. Thus, our study proposes that the adoption of cloud ERP should be examined as a multi-stage process. Using the Theory of Planned Behaviour (TPB) and Ettlie’s adoption stages, as well as employing data gathered from 162 owners of SMEs, our findings show that the factors that influence the intention to adopt cloud ERP vary significantly across adoptive stages.

Nondiffusive Quantum Transport in a Dynamically Disordered Medium

For a dynamically disordered continuum it is found that the exact quantum mechanical mean square displacement 〈x2(t)〉∼t3, for t→∞. A Gaussian white-noise spectrum is assumed for the random potential. The result differs qualitatively from the diffusive behavior well known for the one-band lattice Hamiltonian, and is understandable in terms of the momentum cutoff inherent in the lattice, simulating a "momentum bath."

Small-scale capture, transport and tank adaptation of live, medium-sized Scombrids using "Tuna Tubes"

The transport of live fish is a crucial step to establish fish culture in captivity, and is especially challenging for species that have not been commonly cultured before, therefore transport and handling methods need to be optimized and tailored. This study describes the use of tuna tubes for small-scale transport of medium-sized pelagic fish from the Scombridae family. Tuna tubes are an array of vertical tubes that hold the fish, while fresh seawater is pumped up the tubes and through the fish mouth and gills, providing oxygen and removing wastes. In this study, 19 fish were captured using rod and line and 42% of the captured fish were transported alive in the custom-designed tuna tubes to an on-shore holding tank: five mackerel tuna (Euthynnus affinis) and three leaping bonito (Cybiosarda elegans). Out of these, just three (15.8% of total fish) acclimatized to the tank's condition. Based on these results, we discuss an improved design of the tuna tubes that has the potential to increase survival rates and enable a simple and low cost method of transporting of live pelagic fish.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Small firm internationalisation and the objective characteristics of managers: An importer's relationship marketing perspective

As a result of competitive pressures, firms are transitioning to international sourcing and initiating complex relationships with suppliers. Despite a lack of inward internationalisation research, there is progressive support for the importance of importing. Heavier focus has been placed on downstream efforts in past years, despite the fact that many factors affecting exporting also influence importing. For small and medium sized enterprises (SME), the psychic distance construct is especially important for internationalisation behaviour but there is little evidence on how perceptual psychic distance, that is the individual’s experiences, influences the buyer-seller relationship. This study draws on internationalisation process theory and commitment-trust theory, in an effort to describe the relationship between objective characteristics (i.e. language, cultural background, education and international experience) and relationship marketing (trust and commitment). The study utilises a holistic, multiple case study design to gain a deeper understanding of the inherent complexities of the relationships in dyads and how objective characteristics, which reduce psychic distance, can facilitate trust and commitment development between importers and exporters.

Cloud computing services for the small and medium enterprises: Key considerations for sourcing sustainable business value

The concept of cloud computing services (CCS) is appealing to small and medium enterprises (SMEs). However, while there is a significant push by various authorities on SMEs to adopt the CCS, knowledge of the key considerations to adopt the CCS is very limited. We use the technology-organization-environment (TOE) framework to suggest that a strategic and incremental intent, understanding the organizational structure and culture, understanding the external factors, and consideration of the human resource capacity can contribute to sustainable business value from CCS. Using survey data, we find evidence of a positive association between these considerations and the CCS-related business objectives. We also find evidence of positive association between the CCS-related business objectives and CCS-related financial objectives. The results suggest that the proposed considerations can ensure sustainable business value from the CCS. This study provides guidance to SMEs on a path to adopting the CCS with the intention of a long-term commitment and achieving sustainable business value from these services.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.

Conrad Summenhart's theory of individual rights and its medieval background

This study focuses on the theory of individual rights that the German theologian Conrad Summenhart (1455-1502) explicated in his massive work Opus septipartitum de contractibus pro foro conscientiae et theologico. The central question to be studied is: How does Summenhart understand the concept of an individual right and its immediate implications? The basic premiss of this study is that in Opus septipartitum Summenhart composed a comprehensive theory of individual rights as a contribution to the on-going medieval discourse on rights. With this rationale, the first part of the study concentrates on earlier discussions on rights as the background for Summenhart s theory. Special attention is paid to language in which right was defined in terms of power . In the fourteenth century writers like Hervaeus Natalis and William Ockham maintained that right signifies power by which the right-holder can to use material things licitly. It will also be shown how the attempts to describe what is meant by the term right became more specified and cultivated. Gerson followed the implications that the term power had in natural philosophy and attributed rights to animals and other creatures. To secure right as a normative concept, Gerson utilized the ancient ius suum cuique-principle of justice and introduced a definition in which right was seen as derived from justice. The latter part of this study makes effort to reconstructing Summenhart s theory of individual rights in three sections. The first section clarifies Summenhart s discussion of the right of the individual or the concept of an individual right. Summenhart specified Gerson s description of right as power, taking further use of the language of natural philosophy. In this respect, Summenhart s theory managed to bring an end to a particular continuity of thought that was centered upon a view in which right was understood to signify power to licit action. Perhaps the most significant feature of Summenhart s discussion was the way he explicated the implication of liberty that was present in Gerson s language of rights. Summenhart assimilated libertas with the self-mastery or dominion that in the economic context of discussion took the form of (a moderate) self-ownership. Summenhart discussion also introduced two apparent extensions to Gerson s terminology. First, Summenhart classified right as relation, and second, he equated right with dominion. It is distinctive of Summenhart s view that he took action as the primary determinant of right: Everyone has as much rights or dominion in regard to a thing, as much actions it is licit for him to exercise in regard to the thing. The second section elaborates Summenhart s discussion of the species dominion, which delivered an answer to the question of what kind of rights exist, and clarified thereby the implications of the concept of an individual right. The central feature in Summenhart s discussion was his conscious effort to systematize Gerson s language by combining classifications of dominion into a coherent whole. In this respect, his treatement of the natural dominion is emblematic. Summenhart constructed the concept of natural dominion by making use of the concepts of foundation (founded on a natural gift) and law (according to the natural law). In defining natural dominion as dominion founded on a natural gift, Summenhart attributed natural dominion to animals and even to heavenly bodies. In discussing man s natural dominion, Summenhart pointed out that the natural dominion is not sufficiently identified by its foundation, but requires further specification, which Summenhart finds in the idea that natural dominion is appropriate to the subject according to the natural law. This characterization lead him to treat God s dominion as natural dominion. Partly, this was due to Summenhart s specific understanding of the natural law, which made reasonableness as the primary criterion for the natural dominion at the expense of any metaphysical considerations. The third section clarifies Summenhart s discussion of the property rights defined by the positive human law. By delivering an account on juridical property rights Summenhart connected his philosophical and theological theory on rights to the juridical language of his times, and demonstrated that his own language of rights was compatible with current juridical terminology. Summenhart prepared his discussion of property rights with an account of the justification for private property, which gave private property a direct and strong natural law-based justification. Summenhart s discussion of the four property rights usus, usufructus, proprietas, and possession aimed at delivering a detailed report of the usage of these concepts in juridical discourse. His discussion was characterized by extensive use of the juridical source texts, which was more direct and verbal the more his discussion became entangled with the details of juridical doctrine. At the same time he promoted his own language on rights, especially by applying the idea of right as relation. He also showed recognizable effort towards systematizing juridical language related to property rights.