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.

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.

The Nature, Origins, and Consequences of Finnish Shame-Proneness: A Grounded Theory Study

Although shame is a universal human emotion and is one of the most difficult emotions to overcome, its origins and nature as well as its effects on psychosocial functioning are not well understood or defined. While psychological and spiritual counselors are aware of the effects and consequences of shame for an individual s internal well-being and social life, shame is often still considered a taboo topic and is not given adequate attention. This study aims to explain the developmental process and effects of shame and shame-proneness for individuals and provide tools for practitioners to work more effectively with their clients who struggle with shame. This study presents the empirical foundation for a grounded theory that describes and explains the nature, origins, and consequences of shame-proneness. The study focused on Finnish participants childhood, adolescence and adulthood experiences and why they developed shame-proneness, what it meant for them as children and adolescents and what it meant for them as adults. The data collection phase of this study began in 2000. The participants were recruited through advertisements in local and country-wide newspapers and magazines. Altogether 325 people responded to the advertisements by sending an essay concerning their shame and guilt experiences. For the present study, 135 essays were selected and from those who sent an essay 19 were selected for in-depth interviews. In addition to essays and interviews, participants personal notebooks and childhood hospital and medical reports as well as their scores on the Internalized Shame Scale were analyzed. The development of shame-proneness and significant experiences and events during childhood and adolescence (e.g., health, parenting and parents behavior, humiliation, bullying, neglect, maltreatment and abuse) are discussed and the connections of shame-proneness to psychological concepts such as self-esteem, attachment, perfectionism, narcissism, submissiveness, pleasing others, heightened interpersonal subjectivity, and codependence are explained. Relationships and effects of shame-proneness on guilt, spirituality, temperament, coping strategies, defenses, personality formation and psychological health are also explicated. In addition, shame expressions and the development of shame triggers as well as internalized and externalized shame are clarified. These connections and developments are represented by the core category lack of gaining love, validation and protection as the authentic self. The conclusions drawn from the study include a categorization of shame-prone Finnish people according to their childhood and adolescent experiences and the characteristics of their shame-proneness and personality. Implications for psychological and spiritual counseling are also discussed. Key words: shame, internalized shame, external shame, shame development, shame triggers, guilt, self-esteem, attachment, narcissism, perfectionism, submissiveness, codependence, childhood neglect, childhood abuse, childhood maltreatment, emotional abuse, sexual abuse, spiritual abuse, psychological well-being

Essays on Labor Market Frictions, Technological Change and Macroeconomic Fluctuations

The dissertation consists of an introductory chapter and three essays that apply search-matching theory to study the interaction of labor market frictions, technological change and macroeconomic fluctuations. The first essay studies the impact of capital-embodied growth on equilibrium unemployment by extending a vintage capital/search model to incorporate vintage human capital. In addition to the capital obsolescence (or creative destruction) effect that tends to raise unemployment, vintage human capital introduces a skill obsolescence effect of faster growth that has the opposite sign. Faster skill obsolescence reduces the value of unemployment, hence wages and leads to more job creation and less job destruction, unambiguously reducing unemployment. The second essay studies the effect of skill biased technological change on skill mismatch and the allocation of workers and firms in the labor market. By allowing workers to invest in education, we extend a matching model with two-sided heterogeneity to incorporate an endogenous distribution of high and low skill workers. We consider various possibilities for the cost of acquiring skills and show that while unemployment increases in most scenarios, the effect on the distribution of vacancy and worker types varies according to the structure of skill costs. When the model is extended to incorporate endogenous labor market participation, we show that the unemployment rate becomes less informative of the state of the labor market as the participation margin absorbs employment effects. The third essay studies the effects of labor taxes on equilibrium labor market outcomes and macroeconomic dynamics in a New Keynesian model with matching frictions. Three policy instruments are considered: a marginal tax and a tax subsidy to produce tax progression schemes, and a replacement ratio to account for variability in outside options. In equilibrium, the marginal tax rate and replacement ratio dampen economic activity whereas tax subsidies boost the economy. The marginal tax rate and replacement ratio amplify shock responses whereas employment subsidies weaken them. The tax instruments affect the degree to which the wage absorbs shocks. We show that increasing tax progression when taxation is initially progressive is harmful for steady state employment and output, and amplifies the sensitivity of macroeconomic variables to shocks. When taxation is initially proportional, increasing progression is beneficial for output and employment and dampens shock responses.

Population dynamics of blue mussels in a variable environment at the edge of their range

Spatial and temporal variation in the abundance of species can often be ascribed to spatial and temporal variation in the surrounding environment. Knowledge of how biotic and abiotic factors operate over different spatial and temporal scales in determining distribution, abundance, and structure of populations lies at the heart of ecology. The major part of the current ecological theory stems from studies carried out in central parts of the distributional range of species, whereas knowledge of how marginal populations function is inadequate. Understanding how marginal populations, living at the edge of their range, function is however in a key position to advance ecology and evolutionary biology as scientific disciplines. My thesis focuses on the factors affecting dynamics of marginal populations of blue mussels (Mytilus edulis) living close to their tolerance limits with regard to salinity. The thesis aims to highlight the dynamics at the edge of the range and contrast these with dynamics in more central parts of the range in order to understand the potential interplay between the central and the marginal part in the focal system. The objectives of the thesis are approached by studies on: (1) factors affecting regional patterns of the species, (2) long-term temporal dynamics of the focal species spaced along a regional salinity gradient, (3) selective predation by increasing populations of roach (Rutilus rutilus) when feeding on their main food item, the blue mussel, (4) the primary and secondary effects of local wave exposure gradients and (5) the role of small-scale habitat heterogeneity as determinants of large-scale pattern. The thesis shows that populations of blue mussels are largely determined by large scale changes in sea water salinity, affecting mainly recruitment success and longevity of local populations. In opposite to the traditional view, the thesis strongly indicate that vertebrate predators strongly affect abundance and size structure of blue mussel populations, and that the role of these predators increases towards the margin where populations are increasingly top-down controlled. The thesis also indicates that the positive role of biogenic habitat modifiers increases towards the marginal areas, where populations of blue mussels are largely recruitment limited. Finally, the thesis shows that local blue mussel populations are strongly dependent on high water turbulence, and therefore, dense populations are constrained to offshore habitats. Finally, the thesis suggests that ongoing sedimentation of rocky shores is detrimental for the species, affecting recruitment success and post-recruit survival, pushing stable mussel beds towards offshore areas. Ongoing large scale changes in the Baltic Sea, especially dilution processes with attendant effects, are predicted to substantially contract the distributional range of the mussel, but also affect more central populations. The thesis shows that in order to understand the functioning of marginal populations, research should (1) strive for multi-scale approaches in order to link ecosystem patterns with ecosystem processes, and (2) challenge the prevailing tenets that origin from research carried out in central areas that may not be valid at the edge.

Short- and long-term consequences of food resources on Ural owl Strix uralensis reproduction

Life-history theory states that although natural selection would favour a maximisation of both reproductive output and life-span, such a combination can not be achieved in any living organism. According to life-history theory the reason for the fact that not all traits can be maximised simultaneously is that different traits compete with each other for resources. These relationships between traits that constrain the simultaneous evolution of two or more traits are called trade-offs. Therefore, during different life-stages an individual needs to optimise its allocation of resources to life-history components such as growth, reproduction and survival. Resource limitation acts on these traits and therefore investment in one trait, e.g. reproduction, reduces the resources available for investment in another trait, e.g. residual reproduction or survival. In this thesis I study how food resources during different stages of the breeding event affect reproductive decisions in the Ural owl (Strix uralensis) and the consequences of these decisions on parents and offspring. The Ural owl is a suitable study species for such studies in natural populations since they are long-lived, site-tenacious, and feed on voles. The vole populations in Fennoscandia fluctuate in three- to four-year cycles, which create a variable food environment for the Ural owls to cope with. The thesis gives new insight in reproductive costs and their consequences in natural animal populations with emphasis on underlying physiological mechanisms. I found that supplementary fed Ural owl parents invest supplemented food resources during breeding in own self-maintenance instead of allocating those resources to offspring growth. This investment in own maintenance instead of improving current reproduction had carry-over effects to the following year in terms of increased reproductive output. Therefore, I found evidence that reduced reproductive costs improves future reproductive performance. Furthermore, I found evidence for the underlying mechanism behind this carry-over effect of supplementary food on fecundity. The supplementary-fed parents reduced their feeding investment in the offspring compared to controls, which enabled the fed female parents to invest the surplus resources in parasite resistance. Fed female parents had lower blood parasite loads than control females and this effect lasted until the following year when also reproductive output was increased. Hence, increased investment in parasite resistance when resources are plentiful has the potential to mediate positive carry-over effects on future reproduction. I further found that this carry-over effect was only present when potentials for future reproduction were good. The thesis also provides new knowledge on resource limitation on maternal effects. I found that increased resources prior to egg laying improve the condition and health of Ural owl females and enable them to allocate more resources to reproduction than control females. These additional resources are not allocated to increase the number of offspring, but instead to improve the quality of each offspring. Fed Ural owl females increased the size of their eggs and allocated more health improving immunological components into the eggs. Furthermore, the increased egg size had long-lasting effects on offspring growth, as offspring from larger eggs were heavier at fledging. Limiting resources can have different short- and long-term consequences on reproductive decisions that affect both offspring number and quality. In long-lived organisms, such as the Ural owl, it appears to be beneficial in terms of fitness to invest in long breeding life-span instead of additional investment in current reproduction. In Ural owls, females can influence the phenotypic quality of the offspring by transferring additional resources to the eggs that can have long-lasting effects on growth.

Spatial ecology of an oak-associated herbivore community : A metacommunity of herbivores

Habitat fragmentation is currently affecting many species throughout the world. As a consequence, an increasing number of species are structured as metapopulations, i.e. as local populations connected by dispersal. While excellent studies of metapopulations have accumulated over the past 20 years, the focus has recently shifted from single species to studies of multiple species. This has created the concept of metacommunities, where local communities are connected by the dispersal of one or several of their member species. To understand this higher level of organisation, we need to address not only the properties of single species, but also establish the importance of interspecific interactions. However, studies of metacommunities are so far heavily biased towards laboratory-based systems, and empirical data from natural systems are urgently needed. My thesis focuses on a metacommunity of insect herbivores on the pedunculate oak Quercus robur a tree species known for its high diversity of host-specific insects. Taking advantage of the amenability of this system to both observational and experimental studies, I quantify and compare the importance of local and regional factors in structuring herbivore communities. Most importantly, I contrast the impact of direct and indirect competition, host plant genotype and local adaptation (i.e. local factors) to that of regional processes (as reflected by the spatial context of the local community). As a key approach, I use general theory to generate testable hypotheses, controlled experiments to establish causal relations, and observational data to validate the role played by the pinpointed processes in nature. As the central outcome of my thesis, I am able to relegate local forces to a secondary role in structuring oak-based insect communities. While controlled experiments show that direct competition does occur among both conspecifics and heterospecifics, that indirect interactions can be mediated by both the host plant and the parasitoids, and that host plant genotype may affect local adaptation, the size of these effects is much smaller than that of spatial context. Hence, I conclude that dispersal between habitat patches plays a prime role in structuring the insect community, and that the distribution and abundance of the target species can only be understood in a spatial framework. By extension, I suggest that the majority of herbivore communities are dependent on the spatial structure of their landscape and urge fellow ecologists working on other herbivore systems to either support or refute my generalization.

Kin selection, social polymorphism, and reproductive allocation in ants

Social groups are common across animal species. The reasons for grouping are straightforward when all individuals gain directly from cooperating. However, the situation becomes more complex when helping entails costs to the personal reproduction of individuals. Kin selection theory has offered a fruitful framework to explain such cooperation by stating that individuals may spread their genes not only through their own reproduction, but also by helping related individuals reproduce. However, kin selection theory also implicitly predicts conflicts when groups consist of non-clonal individuals, i.e. relatedness is less than one. Then, individual interests are not perfectly aligned, and each individual is predicted to favour the propagation of their own genome over others. Social insects provide a solid study system to study the interplay between cooperation and conflict. Breeding systems in social insects range from solitary breeding to eusocial colonies displaying complete division of reproduction between the fertile queen and the sterile worker caste. Within colonies, additional variation is provided by the presence of several reproductive individuals. In many species, the queen mates multiply, which causes the colony to consist of half-sib instead of full-sib offspring. Furthermore, in many species colonies contain multiple breeding queens, which further dilutes relatedness between colony members. Evolutionary biology is thus faced with the challenge to answer why such variation in social structure exists, and what the consequences are on the individual and population level. The main part of this thesis takes on this challenge by investing the dynamics of socially polymorphic ant colonies. The first four chapters investigate the causes and consequences of different social structures, using a combination of field studies, genetic analyses and laboratory experiments. The thesis ends with a theoretical chapter focusing on different social interactions (altruism and spite), and the evolution of harming traits. The main results of the thesis show that social polymorphism has the potential to affect the behaviour and traits of both individuals and colonies. For example, we found that genetic polymorphism may increase the phenotypic variation between individuals in colonies, and that socially polymorphic colonies may show different life history patterns. We also show that colony cohesion may be enhanced even in multiple-queen colonies through patterns of unequal reproduction between queens. However, the thesis also demonstrates that spatial and temporal variation between both populations and environments may affect individual and colony traits, to the degree that results obtained in one place or at one time may not be applicable in other situations. This opens up potential further areas of research to explain these differences.

Modeling of Surface UV Radiation Using Satellite Data

Solar UV radiation is harmful for life on planet Earth, but fortunately the atmospheric oxygen and ozone absorb almost entirely the most energetic UVC radiation photons. However, part of the UVB radiation and much of the UVA radiation reaches the surface of the Earth, and affect human health, environment, materials and drive atmospheric and aquatic photochemical processes. In order to quantify these effects and processes there is a need for ground-based UV measurements and radiative transfer modeling to estimate the amounts of UV radiation reaching the biosphere. Satellite measurements with their near-global spatial coverage and long-term data conti-nuity offer an attractive option for estimation of the surface UV radiation. This work focuses on radiative transfer theory based methods used for estimation of the UV radiation reaching the surface of the Earth. The objectives of the thesis were to implement the surface UV algorithm originally developed at NASA Goddard Space Flight Center for estimation of the surface UV irradiance from the meas-urements of the Dutch-Finnish built Ozone Monitoring Instrument (OMI), to improve the original surface UV algorithm especially in relation with snow cover, to validate the OMI-derived daily surface UV doses against ground-based measurements, and to demonstrate how the satellite-derived surface UV data can be used to study the effects of the UV radiation. The thesis consists of seven original papers and a summary. The summary includes an introduction of the OMI instrument, a review of the methods used for modeling of the surface UV using satellite data as well as the con-clusions of the main results of the original papers. The first two papers describe the algorithm used for estimation of the surface UV amounts from the OMI measurements as well as the unique Very Fast Delivery processing system developed for processing of the OMI data received at the Sodankylä satellite data centre. The third and the fourth papers present algorithm improvements related to the surface UV albedo of the snow-covered land. Fifth paper presents the results of the comparison of the OMI-derived daily erythemal doses with those calculated from the ground-based measurement data. It gives an estimate of the expected accuracy of the OMI-derived sur-face UV doses for various atmospheric and other conditions, and discusses the causes of the differences between the satellite-derived and ground-based data. The last two papers demonstrate the use of the satellite-derived sur-face UV data. Sixth paper presents an assessment of the photochemical decomposition rates in aquatic environment. Seventh paper presents use of satellite-derived daily surface UV doses for planning of the outdoor material weathering tests.