The main technical problem with background independent approaches to quantum gravity is inapplicability of standard quantum field theory methods. New methods are needed which would be adapted to the basic principles of General Relativity. Topological field theory is a model which provides natural tools for background independent quantum gravity. It is exactly soluble and, at the same time, diffeomorphism invariant. Applications of topological field theory to quantum gravity include description of boundary states of quantum General Relativity, formulation of quantum gravity as a constrained topological field theory, and a new perturbation theory which uses topological field theory as a starting point. The later is the central theme of the thesis. Unlike the traditional perturbation theory it does not require splitting metric into a background and fluctuations, it is exactly diffeomorphism invariant order by order, and the coupling constant of this theory is dimensionless. We describe the basic ideas and techniques of this perturbation theory as well as inclusion of matter particles, boundary states, and other necessary tools for studying scattering problem in background independent quantum gravity.

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. <br /><br /> Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden <em>SL</em>(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the <em>C</em>-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalizing the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalizations of Kaluza-Klein magnetic monopoles, generalizing the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalizing the known Reissner-Nordström solutions.

We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.

This thesis studies matter emergent as topological excitations of quantum geometry in quantum gravity models. In these models, states are framed four-valent spin networks embedded in a topological three manifold, and the local evolution moves are dual Pachner moves. We first formulate our theory of embedded framed four-valent spin networks by proposing a new graphic calculus of these networks. With this graphic calculus, we study the equivalence classes and the evolution of these networks, and find what we call 3-strand braids, as topological excitations of embedded four-valent spin networks. Each 3-strand braid consists of two nodes that share three edges that may or may not be braided and twisted. The twists happen to be in units of 1/3. Under certain stability condition, some 3-strand braids are stable. Stable braids have rich dynamics encoded in our theory by dual Pachner moves. Firstly, all stable braids can propagate as induced by the expansion and contraction of other regions of their host spin network under evolution. Some braids can also propagate actively, in the sense that they can exchange places with substructures adjacent to them in the graph under the local evolution moves. Secondly, two adjacent braids may have a direct interaction: they merge under the evolution moves to form a new braid if one of them falls into a class called actively interacting braids. The reverse of a direct interaction may happen too, through which a braid decays to another braid by emitting an actively interacting braid. Thirdly, two neighboring braids may exchange a virtual actively interacting braid and become two different braids, in what is called an exchange interaction. Braid dynamics implies an analogue between actively interacting braids and bosons. We also invent a novel algebraic formalism for stable braids. With this new tool, we derive conservation laws from interactions of the braid excitations of spin networks. We show that actively interacting braids form a noncommutative algebra under direction interaction. Each actively interacting braid also behaves like a morphism on non-actively interacting braids. These findings reinforce the analogue between actively interacting braids and bosons. Another important discovery is that stable braids admit seven, and only seven, discrete transformations that uniquely correspond to analogues of C, P, T, and their products. Along with this finding, a braid's electric charge appears to be a function of a conserved quantity, effective twist, of the braids, and thus is quantized in units of 1/3. In addition, each $CPT$-multiplet of actively interacting braids has a unique, characteristic non-negative integer. Braid interactions turn out to be invariant under C, P, and T. Finally, we present an effective description, based on Feynman diagrams, of braid dynamics. This language manifests the analogue between actively interacting braids and bosons, as the topological conservation laws permit them to be singly created and destroyed and as exchanges of these excitations give rise to interactions between braids that are charged under the topological conservation rules. Additionally, we find a constraint on probability amplitudes of braid interactions. We discuss some subtleties, open issues, future directions, and work in progress at the end.

The purpose of this research was to empirically examine the impacts that the presence of a state trading enterprise (STE) has in the international wheat market. There are numerous types of STEs that function in different ways to achieve many different types of policy objectives which are often unique to a particular STE. Although the existence of a STE is justified by the countries involved using numerous policy rationales, the fear that they are used as a front for trade protectionism is a prevalent concern. One specific aspect of a STE that often brings this concern to the forefront is whether or not the STE has the exclusive privilege of monopoly status.<p>The empirical objective of this thesis was to determine specifically if the use of a STE exporter has had a positive impact on world wheat trade over the 1970 2005 period and if the use of a STE importer has had a negative impact. In addition, the marginal impact of the STE having monopoly status was tested. In all cases, the designation of STEs and their monopoly status is based on WTO notification documentations. To secure econometrically robust results, a modified conventional gravity model was chosen. This model was estimated using pooled OLS and fixed effects, the latter consisting of both time and country pair fixed effects. The data that was constructed was a large panel data set of bilateral wheat trade spanning from 1970 to 2005. The model was also tested on a number of subsamples representing countries at different stages of development and in different income categories to isolate potential differences in STEs objectives and impacts.<p>In virtually all models, the presence of a STE exporter had a strongly significant and positive effect on the value and volume of wheat exports from the country with the STE exporter. The fact that a STE had monopoly status did not have any additional impact on wheat trade. The impact of STE importers was insignificant.

This study explores the impact of economic downturn in the EU-27 on Syrian trade and the sensitivity of oil and petroleum products to this downturn. This is carried out using a derivation of the gravity model to determine the export demand. Syrian export with its top 30 trading partners as well as the EU-27 are taken into consideration along with various other trade determinants when measuring the changes in total export volume. The study finds that EU-27 is an important source of demand for Syria, but a downturn in the EU economy will not necessarily have a detrimental effect on Syrian economy. On the other hand, oil plays a far more important role on the country’s exports and its demand is less sensitive to economic fluctuations.

This paper tests the relationship between income inequality and trade flows. The model is based upon Helena Bohman and Désirée Nilsson (2007) and Mitra Trindade and Dalgin (2008). This paper will set up gravity model for 50 countries which includes, income distribution, population, average individual income level and GINI variable as distribution of disposable income as an explanatory variables. Results confirm that when income inequality increases in the exporting country, export of necessities increase and export of luxuries decrease. Income distribution also shows expected effect on trade flows in the importing country. When income inequality increases in the importing country, import of necessities decrease and import of luxuries increase.

There has been much research regarding Trade Immigrant link for different countries, states and provinces which reveal that Immigration impacts bilateral Trade positively. In this study the Trade –Immigrant for Sweden for a period of 2000-2011 for 184 trading partners has been tested which shows that trade and Immigration have positive relationship. Using random effect model, with every 10% increase in Immigrants, there is 4.0% increase in imports and 4.4% increase in exports of Sweden from particular trading partner. In second hypothesis of the study Trade-Emigrant link for Sweden and its 185 trading partners has been checked in cross country sample for year 2010.To the best of my knowledge, this study is first to test the Trade-Emigrant link for Sweden. The results show that there is positive link between trade and Emigration from Sweden. An extended Gravity Model has been used in this study. Using ordinary least square method, with every 10% increase in Emigrants, there is 7.2% increase in imports and 4.3% increase in exports of Sweden for that particular trading partner.

This thesis examines the bilateral trade between Vietnam and twenty three European countries based on a gravity model and panel data for years 1993 to 2004. Estimates indicate that economic size, market size and real exchange rate of Vietnam and twenty three European countries play major role in bilateral trade between Vietnam and these countries. Distance and history, however, do not seem to drive the bilateral trade. The results of gravity model are also applied to calculate the trade potential between Vietnam and twenty three European countries. It shows that Vietnam’s trade with twenty three European countries has considerable room for growth.

This paper investigates the impact of inward FDI (Foreign Direct Investment) on international trade of China empirically on the country level by using panel data from 1984 to 2007. Two separate transformed models which are based on the gravity equation and refer to the econometric models of some previous studies, are used in this paper to estimate the effect of FDI inflows on exports and imports respectively. The estimation results confirmed the complementary relationship between FDI inflows and trade of China both on exports and imports, which has also been supported by previous empirical studies.