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.

Yksilöllisyys ja yhteisöllisyys K. E. Nipkowin uskonnonpedagogisen teorian kehityksessä 1960-1990

Individuality and the Community in the Development of K. E. Nipkow's Theory of Religious Education from 1960 to 1990 The purpose of this study was to describe and analyze the development occurred between 1960 and 1990 of the theory of religious education as proposed by K. E. Nipkow, the German Religious Education specialist, from the point of view of individuality and the community. Nipkow's methodological approach of dialectic convergence theory resulted in a dialogue between theological and educational factors, which supported the thirty-year development of Nipkow's models, theoretical foundations, and theory of religious education. Nipkow's doctoral dissertation, published in 1960, deals with individuality in the thinking of Pestalozzi, Humboldt and Schleiermacher. Nipkow regarded individuality as one of the basic concepts of education, which were to be interpreted anew as social and historical situations changed. In the late 1960s Nipkow developed the so-called experiential hermeneutically oriented context model for the needs of religious education. In this model, individuality is expressed in the attention paid to pupils' life situations and the educational reality. The multi-dimensional theoretical framework of religious education in 1975 emphasized supporting identity as a fundamental task of religious education. The concept of individuality was thus given a new form, in accordance with contemporary theories of developmental psychology. Other fundamental tasks, such as the socio-ethical task, the task of critical religious thinking, and that of ecumenical learning, meant a more specific emphasis on the community. It was an outline of a liberating education, which faced the individualistic-existential and social-ecclesiastical challenges of the time with a critical attitude. The further development of the theoretical outline in 1982 continued to uphold the perspectives of both individuality and the community, as Nipkow combined a historical-social dimension with theories of developmental psychology, especially that of life-span research. According to him, the development of the individual and communal life-reality belonged together. The fundamental task of religious education came to be learning to live and believe together. Nipkow transferred the idea of dialogue into inter-generational learning and developed elementarization as a methodology of Religious Education, which takes into account the point of departure of each age group. His theory of educational responsibility in the church (1990) contained the tasks of walking alongside the individual and the renewal of church communities as prerequisites of communicating the Christian faith in an era characterized by multifaceted Christianity. The "geisteswissenschaftliche" school and its concepts (Ger. Individualität; Bildung) were found to be the explanatory factor of the concepts of individuality and the community in the development of Nipkow's theory of religious education. The concept of education employed by Nipkow (Ger. Bildung) implies, on one hand, the individuality, autonomy, freedom and personal responsibility of people of different ages, and on the other hand, the dialogical nature of education in the community facilitated by this concept. Theologically, Nipkow associates himself in his views on individuality and the community with Schleiermacher's understanding of faith, of which openness towards the world was characteristic. The significance of individuality and the community in Nipkow's thinking was, furthermore, deepened by his participation, as a member of working parties, in the educational discussions of the World Council of Churches.

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

Towards a Critique of the Concept of the Right to Self-Determination in Africa : A Conceptual Examination and the Cases of Western Sahara, Southern Sudan and Eritrea

This thesis examines the right to self-determination which is a norm used for numerous purposes by multiple actors in the field of international relations, with relatively little clarity or agreement on the actual and potential meaning of the right. In international practice, however, the main focus in applying the right has been in the context of decolonization as set by the United Nations in its early decades. Thus, in Africa the right to self-determination has traditionally implied that the colonial territories, and particularly the populations within these territories, were to constitute the people who were entitled to the right. That is, self-determination by decolonization provided a framework for the construction of independent nation-states in Africa whilst other dimensions of the right remained largely or totally neglected. With the objective of assessing the scope, content, developments and interpretations of the right to self-determination in Africa, particularly with regard to the relevance of the right today, the thesis proceeds on two fundamental hypotheses. The first is that Mervyn Frost s theory of settled norms, among which he lists the right to self-determination, assumes too much. Even if the right to self-determination is a human right belonging to all peoples stipulated, inter alia, in the first Article of the 1966 International Human Rights Covenants, it is a highly politicized and context-bound right instead of being settled and observed in a way that its denial would need special justification. Still, the suggested inconsistency or non-compliance with the norm of self-determination is not intended to prove the uselessness or inappropriateness of the norm, but, on the contrary, to invite and encourage debate on the potential use and coverage of the right to self-determination. The second hypothesis is that within the concept of self-determination there are two normative dimensions. One is to do with the idea and practice of statehood, the nation and collectivity that may decide to conduct itself as an independent state. The other one is to do with self-determination as a human right, as a normative condition, to be enjoyed by people and peoples within states that supersedes state authority. These external and internal dimensions need to be seen as complementary and co-terminous, not as mutually exclusive alternatives. The thesis proceeds on the assumption that the internal dimension of the right, with human rights and democracy at its core, has not been considered as important as the external. In turn, this unbalanced and selective interpretation has managed to put the true normative purpose of the right making the world better and bringing more just polity models into a somewhat peculiar light. The right to self-determination in the African context is assessed through case studies of Western Sahara, Southern Sudan and Eritrea. The study asks what these cases say about the right to self-determination in Africa and what their lessons learnt could contribute to the understanding and relevance of the right in today s Africa. The study demonstrates that even in the context of decolonization, the application of the right to self-determination has been far from the consistent approach supposedly followed by the international community: in many respects similar colonial histories have easily led to rather different destinies. While Eritrea secured internationally recognized right to self-determination in the form of retroactive independence in 1993, international recognition of distinct Western Sahara and Southern Sudan entities is contingent on complex and problematic conditions being satisfied. Overall, it is a considerable challenge for international legality to meet empirical political reality in a meaningful way, so that the universal values attached to the norm of self-determination are not overlooked or compromised but rather reinforced in the process of implementing the right. Consequently, this thesis seeks a more comprehensive understanding of the right to self-determination with particular reference to post-colonial Africa and with an emphasis on the internal, human rights and democracy dimensions of the norm. It is considered that the right to self-determination cannot be perceived only as an inter-state issue as it is also very much an intra-state issue, including the possibility of different sub-state arrangements exercised under the right, for example, in the form of autonomy. At the same time, the option of independent statehood achieved through secession remains a mode of exercising and part of the right to self-determination. But in whatever form or way applied, the right to self-determination, as a normative instrument, should constitute and work as a norm that comprehensively brings more added value in terms of the objectives of human rights and democracy. From a normative perspective, a peoples right should not be allowed to transform and convert itself into a right of states. Finally, in light of the case studies of Western Sahara, Southern Sudan and Eritrea, the thesis suggests that our understanding of the right to self-determination should now reach beyond the post-colonial context in Africa. It appears that both the questions and answers to the most pertinent issues of self-determination in the cases studied must be increasingly sought within the postcolonial African state rather than solely in colonial history. In this vein, the right to self-determination can be seen not only as a tool for creating states but also as a way to transform the state itself from within. Any such genuinely post-colonial approach may imply a judicious reconsideration, adaptation or up-dating of the right and our understanding of it in order to render it meaningful in Africa today.

Valtion taiteilijatuki taiteilijan määrittelijänä : Määrittelyvallan ehtoja ja ulottuvuuksia pohjoismaisen tukimallin suomalaisessa muunnelmassa

The dissertation studies state support for artists in the context of the societal process of producing definitions of the artist. It examines the dimensions of and conditions for the power of definition inherent in the Nordic model of artists' support. The dissertation consists of a summary in Finnish and five articles published in English. The theoretical framework is based on Pierre Bourdieu's theory of the fields of cultural production and the concept of artistic classification systems introduced by Paul DiMaggio. The framework also makes use of the analyses by Per Mangset and Dag Solhjell of the relationship between Norwegian artistic fields and the state policy of supporting art. The study assumes that an examination of the formulation and content of the policy of support is insufficient, and extends the analysis to the implementation of the policy both at the level of the structures of decision making and at the level of actual decisions and their impacts. The analysis of the economic dimension of the definition power of artists' support uses register-based data on artists' financial situation. Survey data is used in studying the attitudes of Finnish artists toward state support for artists. The analysis of the Nordic policy of supporting artists uses data based on documents and interviews concerning the formulation and implementation of the policy in Denmark, Finland, Norway and Sweden. The cross-country comparison contributes to identifying the specific features of the Finnish policy of supporting artists from the point of view of its potential power of definition. The study concludes that the legitimating arguments, goals and means of the policy of supporting artists, as well as the structures and actions of the bodies implementing the policy, have an impact on the formulation of definitions of the artist. For example, a relevant factor in this context seems to be the way in which the relationship between various fields of art and the system of support is organized. According to the comparative analysis, the greater the correspondence between the administrative structures of decision making and the organizational structure of artistic fields, the greater the resistance to change regarding the artistic categories produced. By contrast, those structures of decision making which require negotiations and compromises between various interests have produced artistic categories that have been more inclined to change. The development of the Finnish system of artists' support over the past few decades can be described as a slow expansion towards new areas of art. However, the demarcations and hierarchies between various fields of art have not lost their significance, and state support for artists still concentrates on the same areas as it did when the policy of supporting artists was established. State support always contains an element of power. According to the study, the Nordic policy of supporting artists has both the material and symbolic power to participate in the production of societal definitions of the artist. The legitimating arguments, goals and means of the Finnish artists' support, as well as the criteria for granting it, strengthen the symbolic dimension of this power also in terms of the symbolic capital valued by the artistic fields. In this sense, it can be said that the state is one of the actors in the Finnish fields of art. The symbolic dimension of the definition power of artists' support is, however, in the last instance derived from the artistic fields, and reinforces on its part the definition power of these fields.

Joseph A. Schumpeter's Theory of Social and Economic Evolution : a Reconstruction and Critique

The book presents a reconstruction, interpretation and critical evaluation of the Schumpeterian theoretical approach to socio-economic change. The analysis focuses on the problem of social evolution, on the interpretation of the innovation process and business cycles and, finally, on Schumpeter s optimistic neglect of ecological-environmental conditions as possible factors influencing social-economic change. The author investigates how the Schumpeterian approach describes the process of social and economic evolution, and how the logic of transformations is described, explained and understood in the Schumpeterian theory. The material of the study includes Schumpeter s works written after 1925, a related part of the commentary literature on these works, and a selected part of the related literature on the innovation process, technological transformations and the problem of long waves. Concerning the period after 1925, the Schumpeterian oeuvre is conceived and analysed as a more or less homogenous corpus of texts. The book is divided into 9 chapters. Chapters 1-2 describe the research problems and methods. Chapter 3 is an effort to provide a systematic reconstruction of Schumpeter's ideas concerning social and economic evolution. Chapters 4 and 5 focus their analysis on the innovation process. In Chapters 6 and 7 Schumpeter's theory of business cycles is examined. Chapter 8 evaluates Schumpeter's views concerning his relative neglect of ecological-environmental conditions as possible factors influencing social-economic change. Finally, chapter 9 draws the main conclusions.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.