Noncommutative Gravitation as a Gauge Theory of Twisted Poincaré Symmetry

Gravitaation kvanttiteorian muotoilu on ollut teoreettisten fyysikkojen tavoitteena kvanttimekaniikan synnystä lähtien. Kvanttimekaniikan soveltaminen korkean energian ilmiöihin yleisen suhteellisuusteorian viitekehyksessä johtaa aika-avaruuden koordinaattien operatiiviseen ei-kommutoivuuteen. Ei-kommutoivia aika-avaruuden geometrioita tavataan myös avointen säikeiden säieteorioiden tietyillä matalan energian rajoilla. Ei-kommutoivan aika-avaruuden gravitaatioteoria voisi olla yhteensopiva kvanttimekaniikan kanssa ja se voisi mahdollistaa erittäin lyhyiden etäisyyksien ja korkeiden energioiden prosessien ei-lokaaliksi uskotun fysiikan kuvauksen, sekä tuottaa yleisen suhteellisuusteorian kanssa yhtenevän teorian pitkillä etäisyyksillä. Tässä työssä tarkastelen gravitaatiota Poincarén symmetrian mittakenttäteoriana ja pyrin yleistämään tämän näkemyksen ei-kommutoiviin aika-avaruuksiin. Ensin esittelen Poincarén symmetrian keskeisen roolin relativistisessa fysiikassa ja sen kuinka klassinen gravitaatioteoria johdetaan Poincarén symmetrian mittakenttäteoriana kommutoivassa aika-avaruudessa. Jatkan esittelemällä ei-kommutoivan aika-avaruuden ja kvanttikenttäteorian muotoilun ei-kommutoivassa aika-avaruudessa. Mittasymmetrioiden lokaalin luonteen vuoksi tarkastelen huolellisesti mittakenttäteorioiden muotoilua ei-kommutoivassa aika-avaruudessa. Erityistä huomiota kiinnitetään näiden teorioiden vääristyneeseen Poincarén symmetriaan, joka on ei-kommutoivan aika-avaruuden omaama uudentyyppinen kvanttisymmetria. Seuraavaksi tarkastelen ei-kommutoivan gravitaatioteorian muotoilun ongelmia ja niihin kirjallisuudessa esitettyjä ratkaisuehdotuksia. Selitän kuinka kaikissa tähänastisissa lähestymistavoissa epäonnistutaan muotoilla kovarianssi yleisten koordinaattimunnosten suhteen, joka on yleisen suhteellisuusteorian kulmakivi. Lopuksi tutkin mahdollisuutta yleistää vääristynyt Poincarén symmetria lokaaliksi mittasymmetriaksi --- gravitaation ei-kommutoivan mittakenttäteorian saavuttamisen toivossa. Osoitan, että tällaista yleistystä ei voida saavuttaa vääristämällä Poincarén symmetriaa kovariantilla twist-elementillä. Näin ollen ei-kommutoivan gravitaation ja vääristyneen Poincarén symmetrian tutkimuksessa tulee jatkossa keskittyä muihin lähestymistapoihin.

Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

Talousmetafysiikan kritiikkiä

Jakke Holvas: A Critique of the Metaphysics of Economy The research problem of this dissertation is the commonly held opinion according to which everything has become a question of economy in the present day. Economy legitimates and justifies. In this study, the pattern of thinking and conceptualizing in which economy figures as the ultimate reason is called the metaphysics of economy. The defining characteristic of the metaphysics of economy is its failure to recognize non-economic rules, ethics, or ways of existence. The sources included in the study cover certain classics of philosophy (Plato, Aristotle, Friedrich Nietzsche) and sociology (Karl Marx, Max Weber, Marcel Mauss), as well as the more recent French social theory (Jean Baudrillard, Michel Foucault). The research methods used are textual analysis and evaluation of concepts by means of historical comparison. The background to the study is given by the views of historians and sociologists according to whom traditional forms have ceased to exist and the market economy become established as the western system of values. The study identifies points of transition from the traditional forms to economic values. In addition, the dissertation focuses on the modern non-economic forms. The study examines the economic and ethical meanings of gift in antiquity in Homer, Plato, and Aristotle. Following Marcel Mauss, the study analyzes the forms and principles of gift exchange. The study also applies Nietzsche’s philosophy to evaluate under what conditions giving a gift becomes an act of exercising power that puts its receiver into debt. The conclusion of the study is that the classics of philosophy and sociology can rightly be interpreted in terms of the metaphysics of economy, but they also offer grounds for criticizing this metaphysics, even alternatives. One such alternative is non-economic archaic ethic. The study delineates a duality between economy and non-economy as well as creating concepts which could be used in the future to critically analyze economy from a position external to the economic system of concepts.

Naiset rajalla : Kyöpeli, Nainen, Naara(s), Neitsyt, Morsian, Akka ja Ämmä Suomen paikannimissä

Women at the boundary. Kyöpeli ( ghost, devil, elf, fairy, enchantress, witch ), Nainen ( woman ), Naara(s) ( female animal, derogatory term for a woman ), Neitsyt ( young, [virgin] woman ), Morsian ( bride ), Akka ( old woman, wife, grandmother ) and Ämmä ( [old] woman, wife, grandmother ) in Finnish place names This study examines a total of about 4,000 Finnish place names which include a specific that refers to a woman: Kyöpeli, Nainen, Naara(s), Neitsyt, Morsian, Akka or Ämmä. The study has two main objectives. First, to interpret the place names in the data, that is, to examine the words included in the data and establish their background and to differentiate names of different ages. In establishing the background of a name, the type of place (e.g. lake, hill or marsh) and its location, as well as the semantics of the feminine specific, are taken into account. The connotations of words referring to a woman are also studied. Words that refer to a woman are often affective and susceptible to changes in meaning, which is reflected in the history of place names. The second main objective is to recognise and highlight mythological place names. Mythology is pivotal for the interpretation of many place names with a feminine specific. The criteria for mythological names have not been explicitly discussed in Finnish onomastics until now, and I seek to determine such criteria in this study with the help of the data. Mythological place names often refer to large and significant natural localities, which are in many cases important boundaries for the community. Names for smaller localities may also be mythological if they refer to a place with a key location or a special topography (e.g. steep or rocky places). I also discuss the stories involved with specific places in the data, such as stories about supernatural beings. Each of the name groups discussed in the study has its own profile. For example, Naara(s) names are so old that naara is no longer understood to refer to a woman. These names have thus often been misinterpreted in onomastics. Names beginning with Morsian, on the other hand, appear to be of fairly recent origin and may be attributed to an international cautionary tale. Names beginning with Nais, Neitsyt, Akka and Ämmä highlight the duality of the data. They include both old names for important natural localities or boundaries and more recent names for modest dwellings, small cultivated areas and useless marshy ponds. This distribution of place names may reflect a cultural shift that changed the status of women in the community.

Toiminta ja tarkoite : Tutkimus suomen pronominista

The study describes the use and meaning of the Finnish demonstrative pronouns, focus being on the pronoun "tämä" (roughly 'this'). The Finnish demonstrative system is a three way one, the other two demonstratives are "tuo" ('that') and "se" ('it'). The data consisted of 12 half hours of video- and tape-recorded face-to-face and telephone conversations. The method for the study was ethnomethodological conversation analysis (CA); in addition to CA, the theoretical framework consisted of functional linguistics and linguistic anthropology. First, the study dealt with the syntactic distribution of the three demonstratives. The pronouns were analysed according to whether they are before or after the verb, and whether they compose an NP on their own or are determinants of a lexical NP. The study suggested that the form and the placement of the NP presents the referent as continuous/discontinuous or given/new. Givenness of a referent was defined as "identified adequately for the purposes of the on-going action". The so-called dislocated utterances were considered separately. It was found that left-dislocations are used for inserting referents in a particular relation to the on-going activity. Right-dislocations offer a solution for the sometimes competing motivations of newness and continuity: they are used for securing the identifiability of a referent that is implied to be continuous. Second, the study focussed on analysing the meaning of the pronouns according to three dimensions of reference: referential, indexical and relational. It was found that the demonstratives can organize interactional or spatial context. When organizing interactional context, the demonstrative pronouns express the role of identifying the referent in relation to the on-going activity. The pronoun "tämä" expresses that the referent is referentially open and the characterization of the referent is given in the on-going turn. Furthermore, it expresses asymmetry of the indexical ground: it expresses that the participants of a conversation do not share a mutual understanding of the activity at that particular time. In addition, the referent of the pronoun "tämä" is central for understanding the on-going action. Centrality could be understood as the relational feature of the pronoun. However, it is a consequence of the referential and indexical features of "tämä". The pronoun "tuo" also expresses referential openness, but it implies indexical symmetry. The pronoun "se" implies that the referent is known enough, and implies indexical symmetry. When used spatially, the pronouns may refer to a physical space or to a situation. They express or imply that the speaker is inside or outside the referent. The pronoun "tämä" implies inclusion, and the pronoun "tuo" expresses exclusion.

Nonverbal predication in Erzya : Studies on morphosyntactic variation and part of speech distinctions

This dissertation consists of four articles and an introduction. The five parts address the same topic, nonverbal predication in Erzya, from different perspectives. The work is at the same time linguistic typology and Uralic studies. The findings based on a large corpus of empirical Erzya data, which was collected using several different methods and included recordings of the spoken language, made it possible for the present study to apply, then test and finally discuss the previous theories based on cross-linguistic data. Erzya makes use of multiple predication patterns which vary from totally analytic to the morphologically very complex. Nonverbal predicate clause types are classified on the basis of propositional acts in clauses denoting class-membership, identity, property and location. The predicates of these clauses are nouns, adjectives and locational expressions, respectively. The following three predication strategies in Erzya nonverbal predication can be identified: i. the zero-copula construction, ii. the predicative suffix construction and iii. the copula construction. It has been suggested that verbs and nouns cannot be clearly distinguished on morphological grounds when functioning as predicates in Erzya. This study shows that even though predicativity must not be considered a sufficient tool for defining parts of speech in any language, the Erzya lexical classes of adjective, noun and verb can be distinguished from each other also in predicate position. The relative frequency and degree of obligation for using the predicative suffix construction decreases when moving left to right on the scale verb adjective/locative noun ( identificational statement). The predicative suffix is the main pattern in the present tense over the whole domain of nonverbal predication in Standard Erzya, but if it is replaced it is most likely to be with a zero-copula construction in a nominal predication. This study exploits the theory of (a)symmetry for the first time in order to describe verbal vs. nonverbal predication. It is shown that the asymmetry of paradigms and constructions differentiates the lexical classes. Asymmetrical structures are motivated by functional level asymmetry. Variation in predication as such adds to the complexity of the grammar. When symmetric structures are employed, the functional complexity of grammar decreases, even though morphological complexity increases. The genre affects the employment of predication strategies in Erzya. There are differences in the relative frequency of the patterns, and some patterns are totally lacking from some of the data. The clearest difference is that the past tense predicative suffix construction occurs relatively frequently in Standard Erzya, while it occurs infrequently in the other data. Also, the predicative suffixes of the present tense are used more regularly in written Standard Erzya than in any other genre. The genre also affects the incidence of the translative in uľ(ń)ems copula constructions. In translations from Russian to Erzya the translative case is employed relatively frequently in comparison to other data. This study reveals differences between the two Mordvinic languages Erzya and Moksha. The predicative suffixes (bound person markers) of the present tense are used more regularly in Moksha in all kinds of nonverbal predicate clauses compared to Erzya. It should further be observed that identificational statements are encoded with a predicative suffix in Moksha, but seldom in Erzya. Erzya clauses are more frequently encoded using zero-constructions, displaying agreement in number only.

Negotiating and Renegotiating Conversational Ground Rules : Formation of an Artifact Designed to Mediate Exploratory Collaboration

This study highlights the formation of an artifact designed to mediate exploratory collaboration. The data for this study was collected during a Finnish adaptation of the thinking together approach. The aim of the approach is to teach pulps how to engage in educationally beneficial form of joint discussion, namely exploratory talk. At the heart of the approach lies a set of conversational ground rules aimed to promote the use of exploratory talk. The theoretical framework of the study is based on a sociocultural perspective on learning. A central argument in the framework is that physical and psychological tools play a crucial role in human action and learning. With the help of tools humans can escape the direct stimulus of the outside world and learn to control ourselves by using tools. During the implementation of the approach, the classroom community negotiates a set of six rules, which this study conceptualizes as an artifact that mediates exploratory collaboration. Prior research done about the thinking together approach has not extensively researched the formation of the rules, which give ample reason to conduct this study. The specific research questions asked were: What kind of negotiation trajectories did the ground rules form during the intervention? What meanings were negotiated for the ground rules during the intervention The methodological framework of the study is based on discourse analysis, which has been specified by adapting the social construction of intertextuality to analyze the meanings negotiated for the created rules. The study has town units of analysis: thematic episode and negotiation trajectory. A thematic episode is a stretch of talk-in-interaction where the participants talk about a certain ground rule or a theme relating to it. A negotiation trajectory is a chronological representation of the negotiation process of a certain ground rule during the intervention and is constructed of thematic episodes. Thematic episodes were analyzed with the adapted intertextuality analysis. A contrastive analysis was done on the trajectories. Lastly, the meanings negotiated for the created rules were compared to the guidelines provided by the approach. The main result of the study is the observation, that the meanings of the created rules were more aligned with the ground rules of cumulative talk, rather than exploratory talk. Although meanings relating also to exploratory talk were negotiated, they clearly were not the dominant form. In addition, the study observed that the trajectories of the rules were non identical. Despite connecting dimensions (symmetry, composition, continuity and explicitness) none of the trajectories shared exactly the same features as the others.

Technicolor

In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Quantum Chemical Studies of Intermolecular Interactions

This thesis studies the intermolecular interactions in (i) boron-nitrogen based systems for hydrogen splitting and storage, (ii) endohedral complexes, A@C60, and (iii) aurophilic dimers. We first present an introduction of intermolecular interactions. The theoretical background is then described. The research results are summarized in the following sections. In the boron-nitrogen systems, the electrostatic interaction is found to be the leading contribution, as 'Coulomb Pays for Heitler and London' (CHL). For the endohedral complex, the intermolecular interaction is formulated by a one-center expansion of the Coulomb operator 1/rab. For the aurophilic attraction between two C2v monomers, a London-type formula was derived by fully accounting for the anisotropy and point-group symmetry of the monomers.

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.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Numerical computation of the module of a quadrilateral

The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics: 1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research. Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.