Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.

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.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Plant communities of field margins : the effects of management and environmental factors on species composition and diversity

Agri-environmental schemes have so far resulted in only minor positive implications for the biodiversity of agricultural environments, in contrast to what has been expected. Land-use intensification has decreased landscape heterogeneity and the amount of semi-natural habitats. Field margins are uncultivated areas of permanent vegetation located adjacent to fields. Since the number of these habitats is high, investing in their quality may result in more diverse agricultural landscapes. Field margins can be considered as multifunctional habitats providing agronomic, environmental and wildlife services. This thesis aimed at examining the plant communities of different types of field margin habitats and the factors affecting their species diversity and composition. The importance of edaphic, spatial and management factors was studied on regional, landscape and habitat scales. Vegetation surveys were conducted on regional and landscape scales and a field experiment on cutting management was conducted on a habitat scale. In field margin plant communities, species appeared to be indicators of high or intermediate soil fertility and moist soil conditions. The plant species diversity found was rather low, compared with most species-rich agricultural habitats in Finland, such as dry meadows. Among regions, land-use history, main production line, natural species and human induced distribution, climate and edaphic factors were elements inducing differences in species composition. The lowest regional species diversity of field margins was related to intensive and long-term cereal production. Management by cutting and removal or grazing had a positive effect on plant species diversity. The positive effect of cutting and removal on species richness was also dependent on the adjacent source of colonizing species. Therefore, in species-poor habitats and landscapes, establishment of margins with diverse seed mixtures can be recommended for enhancing the development of species richness. However, seed mixtures should include only native species preferably local origin. Management by cutting once a year for 5 years did not result in a decline in dominance of a harmful weed species, Elymus repens, showing that E. repens probably needs cutting more frequently than once per year. Agri-environmental schemes should include long-term contracts with farmers for the establishment, and management by cutting and removal or grazing, of field margins that are several metres wide. In such schemes, the timing and frequency of management should be planned so as not to harm other taxa, such as the insects and birds that are dependent on these habitats. All accidental herbicide drifts to field margins should be avoided when spraying the cultivated area to minimize the negative effects of sprayings on vegetation. The harmful effects of herbicides can be avoided by organic farming methods.

Assessment of insect occurrence in boreal forests based on satellite imagery and field measurements.

The presence/absence data of twenty-seven forest insect taxa (e.g. Retinia resinella, Formica spp., Pissodes spp., several scolytids) and recorded environmental variation were used to investigate the applicability of modelling insect occurrence based on satellite imagery. The sampling was based on 1800 sample plots (25 m by 25 m) placed along the sides of 30 equilateral triangles (side 1 km) in a fragmented forest area (approximately 100 km2) in Evo, S Finland. The triangles were overlaid on land use maps interpreted from satellite images (Landsat TM 30 m multispectral scanner imagery 1991) and digitized geological maps. Insect occurrence was explained using either environmental variables measured in the field or those interpreted from the land use and geological maps. The fit of logistic regression models varied between species, possibly because some species may be associated with the characteristics of single trees while other species with stand characteristics. The occurrence of certain insect species at least, especially those associated with Scots pine, could be relatively accurately assessed indirectly on the basis of satellite imagery and geological maps. Models based on both remotely sensed and geological data better predicted the distribution of forest insects except in the case of Xylechinus pilosus, Dryocoetes sp. and Trypodendron lineatum, where the differences were relatively small in favour of the models based on field measurements. The number of species was related to habitat compartment size and distance from the habitat edge calculated from the land use maps, but logistic regressions suggested that other environmental variables in general masked the effect of these variables in species occurrence at the present scale.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Effect of GPS on understanding relationship between mobile map and environment : A field experiment

Objectives: GPS technology enables the visualisation of a map reader s location on a mobile map. Earlier research on the cognitive aspects of map reading identified that searching for map-environment points is an essential element for the process of determining one s location on a mobile map. Map-environment points refer to objects that are visualized on the map and are recognizable in the environment. However, because the GPS usually adds only one point to the map that has a relation to the environment, it does not provide a sufficient amount of information for self-location. The aim of the present thesis was to assess the effect of GPS on the cognitive processes involved in determining one s location on a map. Methods: The effect of GPS on self-location was studied in a field experiment. The subjects were shown a target on a mobile map, and they were asked to point in the direction of the target. In order for the map reader to be able to deduce the direction of the target, he/she has to locate himself/herself on the map. During the pointing tasks, the subjects were asked to think aloud. The data from the experiment were used to analyze the effect of the GPS on the time needed to perform the task. The subjects verbal data was used to assess the effect of the GPS on the number of landmark concepts mentioned during a task (landmark concepts are words referring to objects that can be recognized both on the map and in the environment). Results and conclusions: The results from the experiment indicate that the GPS reduces the time needed to locate oneself on a map. The analysis of the verbal data revealed that the GPS reduces the number of landmark concepts in the protocols. The findings suggest that the GPS guides the subject s search for the map-environment points and narrows the area on the map that must be searched for self-location.

Overwintering ecology of northern field layer plants : snow and photosynthesis in Vaccinium vitis-idaea L.

Winter is a significant period for the seasonality of northern plants, but is often overlooked when studying the interactions of plants and their environment. This study focuses on the effects of overwintering conditions, including warm winter periods, snow, and snowmelt on boreal and sub-Arctic field layer plants. Wintertime photosynthesis and related physiological factors of evergreen dwarf shrubs, particularly of Vaccinium vitis-idaea, are emphasised. The work combines experiments both in the field and in growth chambers with measurements in natural field conditions. Evergreen dwarf shrubs are predominantly covered by snow in the winter. The protective snow cover provides favourable conditions for photosynthesis, especially during the spring before snowmelt. The results of this study indicate that photosynthesis occurs under the snow in V. vitis-idaea. The light response of photosynthesis determined in field conditions during the period of snow cover shows that positive net CO2 exchange is possible under the snow in the prevailing light and temperature. Photosynthetic capacity increases readily during warm periods in winter and the plants are thus able to replenish carbohydrate reserves lost through respiration. Exposure to low temperatures in combination with high light following early snowmelt can set back photosynthesis as sustained photoprotective measures are activated and photodamage begins to build up. Freezing may further decrease the photosynthetic capacity. The small-scale distribution of many field layer plants, including V. vitis-idaea and other dwarf shrubs, correlates with the snow distribution in a forest. The results of this study indicate that there are species-specific differences in the snow depth affinity of the field and ground layer species. Events and processes taking place in winter can have a profound effect on the overall performance of plants and on the interactions between plants and their environment. Understanding the processes involved in the overwintering of plants is increasingly important as the wintertime climate in the north is predicted to change in the future.

Field intercomparison of four methane gas analysers suitable for eddy covariance flux measurements

Eddy covariance (EC)-flux measurement technique is based on measurement of turbulent motions of air with accurate and fast measurement devices. For instance, in order to measure methane flux a fast methane gas analyser is needed which measures methane concentration at least ten times in a second in addition to a sonic anemometer, which measures the three wind components with the same sampling interval. Previously measurement of methane flux was almost impossible to carry out with EC-technique due to lack of fast enough gas analysers. However during the last decade new instruments have been developed and thus methane EC-flux measurements have become more common. Performance of four methane gas analysers suitable for eddy covariance measurements are assessed in this thesis. The assessment and comparison was performed by analysing EC-data obtained during summer 2010 (1.4.-26.10.) at Siikaneva fen. The four participating methane gas analysers are TGA-100A (Campbell Scientific Inc., USA), RMT-200 (Los Gatos Research, USA), G1301-f (Picarro Inc., USA) and Prototype-7700 (LI-COR Biosciences, USA). RMT-200 functioned most reliably throughout the measurement campaign and the corresponding methane flux data had the smallest random error. In addition, methane fluxes calculated from data obtained from G1301-f and RMT-200 agree remarkably well throughout the measurement campaign. The calculated cospectra and power spectra agree well with corresponding temperature spectra. Prototype-7700 functioned only slightly over one month in the beginning of the measurement campaign and thus its accuracy and long-term performance is difficult to assess.