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.

Noncommutative Quantum Field Theories and UV/IR Mixing

Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

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.

On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Formation of structure in dark energy cosmologies

Acceleration of the universe has been established but not explained. During the past few years precise cosmological experiments have confirmed the standard big bang scenario of a flat universe undergoing an inflationary expansion in its earliest stages, where the perturbations are generated that eventually form into galaxies and other structure in matter, most of which is non-baryonic dark matter. Curiously, the universe has presently entered into another period of acceleration. Such a result is inferred from observations of extra-galactic supernovae and is independently supported by the cosmic microwave background radiation and large scale structure data. It seems there is a positive cosmological constant speeding up the universal expansion of space. Then the vacuum energy density the constant describes should be about a dozen times the present energy density in visible matter, but particle physics scales are enormously larger than that. This is the cosmological constant problem, perhaps the greatest mystery of contemporary cosmology. In this thesis we will explore alternative agents of the acceleration. Generically, such are called dark energy. If some symmetry turns off vacuum energy, its value is not a problem but one needs some dark energy. Such could be a scalar field dynamically evolving in its potential, or some other exotic constituent exhibiting negative pressure. Another option is to assume that gravity at cosmological scales is not well described by general relativity. In a modified theory of gravity one might find the expansion rate increasing in a universe filled by just dark matter and baryons. Such possibilities are taken here under investigation. The main goal is to uncover observational consequences of different models of dark energy, the emphasis being on their implications for the formation of large-scale structure of the universe. Possible properties of dark energy are investigated using phenomenological paramaterizations, but several specific models are also considered in detail. Difficulties in unifying dark matter and dark energy into a single concept are pointed out. Considerable attention is on modifications of gravity resulting in second order field equations. It is shown that in a general class of such models the viable ones represent effectively the cosmological constant, while from another class one might find interesting modifications of the standard cosmological scenario yet allowed by observations. The thesis consists of seven research papers preceded by an introductory discussion.

Representing the epistemic nature of teachers’ practical knowledge : The case of class teachers’ general pedagogy

The present study addressed the epistemology of teachers’ practical knowledge. Drawing from the literature, teachers’ practical knowledge is defined as all teachers’ cognitions (e.g., beliefs, values, motives, procedural knowing, and declarative knowledge) that guide their practice of teaching. The teachers’ reasoning that lies behind their practical knowledge is addressed to gain insight into its epistemic nature. I studied six class teachers’ practical knowledge; they teach in the metropolitan region of Helsinki. Relying on the assumptions of the phenomenographic inquiry, I collected and analyzed the data. I analyzed the data in two stages where the first stage involved an abductive procedure, and the second stage an inductive procedure for interpretation, and thus developed the system of categories. In the end, a quantitative analysis nested into the qualitative findings to study the patterns of the teachers’’ reasoning. The results indicated that teachers justified their practical knowledge based on morality and efficiency of action; efficiency of action was found to be presented in two different ways: authentic efficiency and naïve efficiency. The epistemic weight of morality was embedded in what I call “moral care”. The core intention of teachers in the moral care was the commitment that they felt about the “whole character” of students. From this perspective the “dignity” and the moral character of the students should not replaced for any other “instrumental price”. “Caring pedagogy” was the epistemic value of teachers’ reasoning in the authentic efficiency. The central idea in the caring pedagogy was teachers’ intentions to improve the “intellectual properties” of “all or most” of the students using “flexible” and “diverse” pedagogies. However, “regulating pedagogy” was the epistemic condition of practice in the cases corresponding to naïve efficiency. Teachers argued that an effective practical knowledge should regulate and manage the classroom activities, but the targets of the practical knowledge were mainly other “issues “or a certain percentage of the students. In these cases, the teachers’ arguments were mainly based on the notion of “what worked” regardless of reflecting on “what did not work”. Drawing from the theoretical background and the data, teachers’ practical knowledge calls for “praxial knowledge” when they used the epistemic conditions of “caring pedagogy” and “moral care”. It however calls for “practicable” epistemic status when teachers use the epistemic condition of regulating pedagogy. As such, praxial knowledge with the dimensions of caring pedagogy and moral care represents the “normative” perspective on teachers’ practical knowledge, and thus reflects a higher epistemic status in comparison to “practicable” knowledge, which represents a “descriptive” perception toward teachers’ practical knowledge and teaching.

Studies of new inorganic species using relativistic quantum chemistry

In the present work the methods of relativistic quantum chemistry have been applied to a number of small systems containing heavy elements, for which relativistic effects are important. First, a thorough introduction of the methods used is presented. This includes some of the general methods of computational chemistry and a special section dealing with how to include the effects of relativity in quantum chemical calculations. Second, after this introduction the results obtained are presented. Investigations on high-valent mercury compounds are presented and new ways to synthesise such compounds are proposed. The methods described were applied to certain systems containing short Pt-Tl contacts. It was possible to explain the interesting bonding situation in these compounds. One of the most common actinide compounds, uranium hexafluoride was investigated and a new picture of the bonding was presented. Furthermore the rareness of uranium-cyanide compounds was discussed. In a foray into the chemistry of gold, well known for its strong relativistic effects, investigations on different gold systems were performed. Analogies between Au$^+$ and platinum on one hand and oxygen on the other were found. New systems with multiple bonds to gold were proposed to experimentalists. One of the proposed systems was spectroscopically observed shortly afterwards. A very interesting molecule, which was theoretically predicted a few years ago is WAu$_{12}$. Some of its properties were calculated and the bonding situation was discussed. In a further study on gold compounds it was possible to explain the substitution pattern in bis[phosphane-gold(I)] thiocyanate complexes. This is of some help to experimentalists as the systems could not be crystallised and the structure was therefore unknown. Finally, computations on one of the heaviest elements in the periodic table were performed. Calculation on compounds containing element 110, darmstadtium, showed that it behaves similarly as its lighter homologue platinum. The extreme importance of relativistic effects for these systems was also shown.

Spirometric studies on the adult general population of Helsinki : bronchodilation responses, determinants, and intrasession repeatability of FEV1, FEV6, FVC, and forced expiratory time

Spirometry is the most widely used lung function test in the world. It is fundamental in diagnostic and functional evaluation of various pulmonary diseases. In the studies described in this thesis, the spirometric assessment of reversibility of bronchial obstruction, its determinants, and variation features are described in a general population sample from Helsinki, Finland. This study is a part of the FinEsS study, which is a collaborative study of clinical epidemiology of respiratory health between Finland (Fin), Estonia (Es), and Sweden (S). Asthma and chronic obstructive pulmonary disease (COPD) constitute the two major obstructive airways diseases. The prevalence of asthma has increased, with around 6% of the population in Helsinki reporting physician-diagnosed asthma. The main cause of COPD is smoking with changes in smoking habits in the population affecting its prevalence with a delay. Whereas airway obstruction in asthma is by definition reversible, COPD is characterized by fixed obstruction. Cough and sputum production, the first symptoms of COPD, are often misinterpreted for smokers cough and not recognized as first signs of a chronic illness. Therefore COPD is widely underdiagnosed. More extensive use of spirometry in primary care is advocated to focus smoking cessation interventions on populations at risk. The use of forced expiratory volume in six seconds (FEV6) instead of forced vital capacity (FVC) has been suggested to enable office spirometry to be used in earlier detection of airflow limitation. Despite being a widely accepted standard method of assessment of lung function, the methodology and interpretation of spirometry are constantly developing. In 2005, the ATS/ERS Task Force issued a joint statement which endorsed the 12% and 200 ml thresholds for significant change in forced expiratory volume in one second (FEV1) or FVC during bronchodilation testing, but included the notion that in cases where only FVC improves it should be verified that this is not caused by a longer exhalation time in post-bronchodilator spirometry. This elicited new interest in the assessment of forced expiratory time (FET), a spirometric variable not usually reported or used in assessment. In this population sample, we examined FET and found it to be on average 10.7 (SD 4.3) s and to increase with ageing and airflow limitation in spirometry. The intrasession repeatability of FET was the poorest of the spirometric variables assessed. Based on the intrasession repeatability, a limit for significant change of 3 s was suggested for FET during bronchodilation testing. FEV6 was found to perform equally well as FVC in the population and in a subgroup of subjects with airways obstruction. In the bronchodilation test, decreases were frequently observed in FEV1 and particularly in FVC. The limit of significant increase based on the 95th percentile of the population sample was 9% for FEV1 and 6% for FEV6 and FVC; these are slightly lower than the current limits for single bronchodilation tests (ATS/ERS guidelines). FEV6 was proven as a valid alternative to FVC also in the bronchodilation test and would remove the need to control duration of exhalation during the spirometric bronchodilation test.

Assessment of Risk for Type 1 Diabetes in Children of Affected Families and in the General Population : Role of Immunological and Metabolic Markers

Background and aims. Type 1 diabetes (T1D), an autoimmune disease in which the insulin producing beta cells are gradually destroyed, is preceded by a prodromal phase characterized by appearance of diabetes-associated autoantibodies in circulation. Both the timing of the appearance of autoantibodies and their quality have been used in the prediction of T1D among first-degree relatives of diabetic patients (FDRs). So far, no general strategies for identifying individuals at increased disease risk in the general population have been established, although the majority of new cases originate in this population. The current work aimed at assessing the predictive role of diabetes-associated immunologic and metabolic risk factors in the general population, and comparing these factors with data obtained from studies on FDRs. Subjects and methods. Study subjects in the current work were subcohorts of participants of the Childhood Diabetes in Finland Study (DiMe; n=755), the Cardiovascular Risk in Young Finns Study (LASERI; n=3475), and the Finnish Type 1 Diabetes Prediction and Prevention Study (DIPP) Study subjects (n=7410). These children were observed for signs of beta-cell autoimmunity and progression to T1D, and the results obtained were compared between the FDRs and the general population cohorts. --- Results and conclusions. By combining HLA and autoantibody screening, T1D risks similar to those reported for autoantibody-positive FDRs are observed in the pediatric general population. Progression rate to T1D is high in genetically susceptible children with persistent multipositivity. Measurement of IAA affinity failed in stratifying the risk assessment in young IAA-positive children with HLA-conferred disease susceptibility, among whom affinity of IAA did not increase during the prediabetic period. Young age at seroconversion, increased weight-for-height, decreased early insulin response, and increased IAA and IA-2A levels predict T1D in young children with genetic disease susceptibility and signs of advanced beta-cell autoimmunity. Since the incidence of T1D continues to increase, efforts aimed at preventing T1D are important, and reliable disease prediction is needed both for intervention trials and for effective and safe preventive therapies in the future. Our observations confirmed that combined HLA-based screening and regular autoantibody measurements reveal similar disease risks in pediatric general population as those seen in prediabetic FDRs, and that risk assessment can be stratified further by studying glucose metabolism of prediabetic subjects. As these screening efforts are feasible in practice, the knowledge now obtained can be exploited while designing intervention trials aimed at secondary prevention of T1D.

Irritable bowel syndrome in the general population : epidemiology, comorbidity and societal costs

Background: Irritable bowel syndrome (IBS) is a common functional gastrointestinal (GI) disorder characterised by abdominal pain and abnormal bowel function. It is associated with a high rate of healthcare consumption and significant health care costs. The prevalence and economic burden of IBS in Finland has not been studied before. The aims of this study were to assess the prevalence of IBS according to various diagnostic criteria and to study the rates of psychiatric and somatic comorbidity in IBS. In addition, health care consumption and societal costs of IBS were to be evaluated. Methods: The study was a two-phase postal survey. Questionnaire I identifying IBS by Manning 2 (at least two of the six Manning symptoms), Manning 3 (at least three Manning symptoms), Rome I, and Rome II criteria, was mailed to a random sample of 5 000 working age subjects. It also covered extra-GI symptoms such as headache, back pain, and depression. Questionnaire II, covering rates of physician visits, and use of GI medication, was sent to subjects fulfilling Manning 2 or Rome II IBS criteria in Questionnaire I. Results: The response rate was 73% and 86% for questionnaires I and II. The prevalence of IBS was 15.9%, 9.6%, 5.6%, and 5.1% according to Manning 2, Manning 3, Rome I, and Rome II criteria. Of those meeting Rome II criteria, 97% also met Manning 2 criteria. Presence of severe abdominal pain was more often reported by subjects meeting either of the Rome criteria than those meeting either of the Manning criteria. Presence of depression, anxiety, and several somatic symptoms was more common among subjects meeting any IBS criterion than by controls. Of subjects with depressive symptoms, 11.6% met Rome II IBS criteria compared to 3.7% of those with no depressiveness. Subjects meeting any IBS criteria made more physician visits than controls. Intensity of GI symptoms and presence of dyspeptic symptoms were the strongest predictors of GI consultations. Presence of dyspeptic symptoms and a history of abdominal pain in childhood also predicted non-GI visits. Annual GI related individual costs were higher in the Rome II group (497 ) than in the Manning 2 group (295 ). Direct expenses of GI symptoms and non GI physician visits ranged between 98M for Rome II and 230M for Manning 2 criteria. Conclusions: The prevalence of IBS varies substantially depending on the criteria applied. Rome II criteria are more restrictive than Manning 2, and they identify an IBS population with more severe GI symptoms, more frequent health care use, and higher individual health care costs. Subjects with IBS demonstrate high rates of psychiatric and somatic comorbidity regardless of health care seeking status. Perceived symptom severity rather than psychiatric comorbidity predicts health care seeking for GI symptoms. IBS incurs considerable medical costs. The direct GI and non-GI costs are equivalent to up to 5% of outpatient health care and medicine costs in Finland. A more integral approach to IBS by physicians, accounting also for comorbid conditions, may produce a more favourable course in IBS patients and reduce health care expenditures.

Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Flow forecasts in general planning of municipal water and sewage works

Vuorokausivirtaaman ennustaminen yhdyskuntien vesi- ja viemärilaitosten yleissuunnittelussa.