Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

On the GKP Vacuum in Gauge/Gravity Correspondences

Within the framework of the AdS5/CFT4 correspondence, the GKP string living on a AdS5 x S5 background finds a counterpart in the anti-ferromagnetic vacuum state for the spin chain, fruitfully employed to investigate the dual N=4 SYM superconformal gauge theory. The thesis mainly deals with the excitations over such a vacuum: dispersion relations and scattering matrices are computed, moreover a set of Asymptotic Bethe Ansatz equations is formulated. Furthermore, the survey of the GKP vacuum within the AdS4/CFT3 duality between a string theory on AdS4 x CP 3 and N=6 Chern-Simons reveals intriguing connections relating the latter to N=4 SYM, in a peculiar high spin limit.

Non-Linear Pricing in Imperfectly Competitive Markets

This thesis is dedicated to the analysis of non-linear pricing in oligopoly. Non-linear pricing is a fairly predominant practice in most real markets, mostly characterized by some amount of competition. The sophistication of pricing practices has increased in the latest decades due to the technological advances that have allowed companies to gather more and more data on consumers preferences. The first essay of the thesis highlights the main characteristics of oligopolistic non-linear pricing. Non-linear pricing is a special case of price discrimination. The theory of price discrimination has to be modified in presence of oligopoly: in particular, a crucial role is played by the competitive externality that implies that product differentiation is closely related to the possibility of discriminating. The essay reviews the theory of competitive non-linear pricing by starting from its foundations, mechanism design under common agency. The different approaches to model non-linear pricing are then reviewed. In particular, the difference between price and quantity competition is highlighted. Finally, the close link between non-linear pricing and the recent developments in the theory of vertical differentiation is explored. The second essay shows how the effects of non-linear pricing are determined by the relationship between the demand and the technological structure of the market. The chapter focuses on a model in which firms supply a homogeneous product in two different sizes. Information about consumers' reservation prices is incomplete and the production technology is characterized by size economies. The model provides insights on the size of the products that one finds in the market. Four equilibrium regions are identified depending on the relative intensity of size economies with respect to consumers' evaluation of the good. Regions for which the product is supplied in a single unit or in several different sizes or in only a very large one. Both the private and social desirability of non-linear pricing varies across different equilibrium regions. The third essay considers the broadband internet market. Non discriminatory issues seem the core of the recent debate on the opportunity or not of regulating the internet. One of the main questions posed is whether the telecom companies, owning the networks constituting the internet, should be allowed to offer quality-contingent contracts to content providers. The aim of this essay is to analyze the issue through a stylized two-sided market model of the web that highlights the effects of such a discrimination over quality, prices and participation to the internet of providers and final users. An overall welfare comparison is proposed, concluding that the final effects of regulation crucially depend on both the technology and preferences of agents.

Welfare provision in Sweden and the dominant position of the Sap

There have been almost fifty years since Harry Eckstein' s classic monograph, A Theory of Stable Democracy (Princeton, 1961), where he sketched out the basic tenets of the “congruence theory”, which was to become one of the most important and innovative contributions to understanding democratic rule. His next work, Division and Cohesion in Democracy, (Princeton University Press: 1966) is designed to serve as a plausibility probe for this 'theory' (ftn.) and is a case study of a Northern democratic system, Norway. What is more, this line of his work best exemplifies the contribution Eckstein brought to the methodology of comparative politics through his seminal article, “ “Case Study and Theory in Political Science” ” (in Greenstein and Polsby, eds., Handbook of Political Science, 1975), on the importance of the case study as an approach to empirical theory. This article demonstrates the special utility of “crucial case studies” in testing theory, thereby undermining the accepted wisdom in comparative research that the larger the number of cases the better. Although not along the same lines, but shifting the case study unit of research, I intend to take up here the challenge and build upon an equally unique political system, the Swedish one. Bearing in mind the peculiarities of the Swedish political system, my unit of analysis is going to be further restricted to the Swedish Social Democratic Party, the Svenska Arbetare Partiet. However, my research stays within the methodological framework of the case study theory inasmuch as it focuses on a single political system and party. The Swedish SAP endurance in government office and its electoral success throughout half a century (ftn. As of the 1991 election, there were about 56 years - more than half century - of interrupted social democratic "reign" in Sweden.) are undeniably a performance no other Social Democrat party has yet achieved in democratic conditions. Therefore, it is legitimate to inquire about the exceptionality of this unique political power combination. Which were the different components of this dominance power position, which made possible for SAP's governmental office stamina? I will argue here that it was the end-product of a combination of multifarious factors such as a key position in the party system, strong party leadership and organization, a carefully designed strategy regarding class politics and welfare policy. My research is divided into three main parts, the historical incursion, the 'welfare' part and the 'environment' part. The first part is a historical account of the main political events and issues, which are relevant for my case study. Chapter 2 is devoted to the historical events unfolding in the 1920-1960 period: the Saltsjoebaden Agreement, the series of workers' strikes in the 1920s and SAP's inception. It exposes SAP's ascent to power in the mid 1930s and the party's ensuing strategies for winning and keeping political office, that is its economic program and key economic goals. The following chapter - chapter 3 - explores the next period, i.e. the period from 1960s to 1990s and covers the party's troubled political times, its peak and the beginnings of the decline. The 1960s are relevant for SAP's planning of a long term economic strategy - the Rehn Meidner model, a new way of macroeconomic steering, based on the Keynesian model, but adapted to the new economic realities of welfare capitalist societies. The second and third parts of this study develop several hypotheses related to SAP's 'dominant position' (endurance in politics and in office) and test them afterwards. Mainly, the twin issues of economics and environment are raised and their political relevance for the party analyzed. On one hand, globalization and its spillover effects over the Swedish welfare system are important causal factors in explaining the transformative social-economic challenges the party had to put up with. On the other hand, Europeanization and environmental change influenced to a great deal SAP's foreign policy choices and its domestic electoral strategies. The implications of globalization on the Swedish welfare system will make the subject of two chapters - chapters four and five, respectively, whereupon the Europeanization consequences will be treated at length in the third part of this work - chapters six and seven, respectively. Apparently, at first sight, the link between foreign policy and electoral strategy is difficult to prove and uncanny, in the least. However, in the SAP's case there is a bulk of literature and public opinion statistical data able to show that governmental domestic policy and party politics are in a tight dependence to foreign policy decisions and sovereignty issues. Again, these country characteristics and peculiar causal relationships are outlined in the first chapters and explained in the second and third parts. The sixth chapter explores the presupposed relationship between Europeanization and environmental policy, on one hand, and SAP's environmental policy formulation and simultaneous agenda-setting at the international level, on the other hand. This chapter describes Swedish leadership in environmental policy formulation on two simultaneous fronts and across two different time spans. The last chapter, chapter eight - while trying to develop a conclusion, explores the alternative theories plausible in explaining the outlined hypotheses and points out the reasons why these theories do not fit as valid alternative explanation to my systemic corporatism thesis as the main causal factor determining SAP's 'dominant position'. Among the alternative theories, I would consider Traedgaardh L. and Bo Rothstein's historical exceptionalism thesis and the public opinion thesis, which alone are not able to explain the half century social democratic endurance in government in the Swedish case.

Higher Chern-Simons gauge theory

Higher gauge theory arises naturally in superstring theory, but many of its features remain obscure. In this thesis, after an exposition of the bacis tools in local higher gauge theory, a higher gauge Chern-Simons model is defined. We discuss the classical equations of motion as well as the behaviour of the gauge anomaly. We perform canonical quantization and we introduce two possible quantization schemes for the model. We also expound higher parallel transport in higher gauge theory, and we speculate that it can provide Wilson surfaces as topological observables for the higher gauge Chern-Simons theory.