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.

Determinants of institutional care at older ages in Finland

Väitöskirjassa selvitettiin ikäihmisten laitoshoitoon siirtymisen todennäköisyyttä ja sen taustoja kansainvälisesti ainutlaatuisen rekisteriaineiston avulla. Selvitettäviä asioita olivat eri sairauksien, sosioekonomisten tekijöiden, puolison olemassaolon ja leskeksi jäämisen yhteys laitoshoitoon siirtymiseen yli 65-vuotiailla suomalaisilla. Tutkimuksessa havaittiin, että dementia, Parkinsonin tauti, aivohalvaus, masennusoireet ja muut mielenterveysongelmat, lonkkamurtuma sekä diabetes lisäsivät ikäihmisten todennäköisyyttä siirtyä laitoshoitoon yli 50 prosentilla, kun muut sairaudet ja sosiodemografiset tekijät oli otettu huomioon. Korkeat tulot vähensivät laitoshoidon todennäköisyyttä, kun taas puutteellinen asuminen (ilman peseytymistiloja tai keskus- tai sähkölämmitystä) sekä erittäin puutteellinen asuminen (ilman lämmintä vettä, vesijohtoa, viemäriä tai vesivessaa) lisäsivät todennäkösyyttä, kun muut sosiodemografiset tekijät, sairaudet ja asuinalue oli huomioitu. Kerrostalon hissittömyys ei ollut yhteydessä laitoshoidon todennäköisyyteen. Todennäköisyys siirtyä laitoshoitoon oli jostain syystä korkeampaa niillä ikäihmisillä, jotka asuivat vuokralla ja matalampaa omakotitalossa asuvilla ja niillä, joilla oli auto. Puolison olemassaolo vähensi ja leskeksi jääminen lisäsi laitoshoidon todennäköisyyttä huomattavasti. Todennäköisyys oli erityisen suuri, yli kolminkertainen, kun puolison kuolemasta oli kulunut enintään kuukausi verrattuna niihin, joiden puoliso oli elossa. Todennäköisyys laski, kun puolison kuolemasta kului aikaa. Miesten ja naisten tulokset olivat samansuuntaisia. Korkeat tulot tai koulutus eivät suojanneet riskiltä joutua laitoshoitoon puolison kuoltua. Puolison kuolema näyttää lisäävän hoidon tarvetta, kun kotona ei ole enää puolisoa tukemassa ja huolehtimassa kodin askareista. Laitoshoidon tarve vähenee, jos ja kun lesket ajan kuluessa oppivat elämään yksin. Toisaalta tutkimustulokset saattavat viitata myös siihen, että kaikkein huonokuntoisimmat lesket, jotka eivät pärjää yksin asuessaan, siirtyvät laitoshoitoon hyvin nopeasti puolison kuoltua. Tutkimuksessa oli mukana yhteensä yli 280 000 yli 65-vuotiasta henkilöä, joiden pitkäaikaiseen laitoshoitoon siirtymistä seurattiin tammikuusta 1998 syyskuuhun 2003. Laitoshoidoksi määriteltiin terveyskeskuksissa, sairaaloissa ja vanhainkodeissa tai vastaavissa yksiköissä tapahtuva pitkäaikainen hoito, joka kesti yli 90 vuorokautta tai oli vahvistettu pitkäaikaishoidon päätöksellä. Tutkimuksessa käytetty aineisto koottiin väestörekistereistä, sosiaali- ja terveydenhuollon rekistereistä ja lääkerekistereistä.

Selective-Area Atomic Layer Deposition

Atomic layer deposition (ALD) is a method to deposit thin films from gaseous precursors to the substrate layer-by-layer so that the film thickness can be tailored with atomic layer accuracy. Film tailoring is even further emphasized with selective-area ALD which enables the film growth to be controlled also on the substrate surface. Selective-area ALD allows the decrease of a process steps in preparing thin film devices. This can be of a great technological importance when the ALD films become into wider use in different applications. Selective-area ALD can be achieved by passivation or activation of a surface. In this work ALD growth was prevented by octadecyltrimethoxysilane, octadecyltrichlorosilane and 1-dodecanethiol SAMs, and by PMMA (polymethyl methacrylate) and PVP (poly(vinyl pyrrolidone) polymer films. SAMs were prepared from vapor phase and by microcontact printing, and polymer films were spin coated. Microcontact printing created patterned SAMs at once. The SAMs prepared from vapor phase and the polymer mask layers were patterned by UV lithography or lift-off process so that after preparation of a continuous mask layer selected areas of them were removed. On these areas the ALD film was deposited selectively. SAMs and polymer films prevented the growth in several ALD processes such as iridium, ruthenium, platinum, TiO2 and polyimide so that the ALD films did grow only on areas without SAM or polymer mask layer. PMMA and PVP films also protected the surface against Al2O3 and ZrO2 growth. Activation of the surface for ALD of ruthenium was achieved by preparing a RuOX layer by microcontact printing. At low temperatures the RuCp2-O2 process nucleated only on this oxidative activation layer but not on bare silicon.

The Effect of Food-Related Lifestyle on the Choices of Consumers of Five Food Products

The purpose of this study was to find out whether food-related lifestyle guides and explains product evaluations, specifically, consumer perceptions and choice evaluations of five different food product categories: lettuce, mincemeat, savoury sauce, goat cheese, and pudding. The opinions of consumers who shop in neighbourhood stores were considered most valuable. This study applies means-end chain (MEC) theory, according to which products are seen as means by which consumers attain meaningful goals. The food-related lifestyle (FRL) instrument was created to study lifestyles that reflect these goals. Further, this research has adopted the view that the FRL functions as a script which guides consumer behaviour. Two research methods were used in this study. The first was the laddering interview, the primary aim of which was to gather information for formulating the questionnaire of the main study. The survey consisted of two separate questionnaires. The first was the FRL questionnaire modified for this study. The aim of the other questionnaire was to determine the choice criteria for buying five different categories of food products. Before these analyses could be made, several data modifications were made following MEC analysis procedures. Beside forming FRL dimensions by counting sum-scores from the FRL statements, factor analysis was run in order to elicit latent factors underlying the dimensions. The lifestyle factors found were adventurous, conscientious, enthusiastic, snacking, moderate, and uninvolved lifestyles. The association analyses were done separately for each choice of product as well as for each attribute-consequence linkage with a non-parametric Mann-Whitney U test. The testing variables were FRL dimensions and the FRL lifestyle factors. In addition, the relation between the attribute-consequence linkages and the demographic variables were analysed. Results from this study showed that the choice of product is sequential, so that consumers first categorize products into groups based on specific criteria like health or convenience. It was attested that the food-related lifestyles function as a script in food choice and that the FRL instrument can be used to predict consumer buying behaviour. Certain lifestyles were associated with the choice of each product category. The actual product choice within a product category then appeared to be a different matter. In addition, this study proposes a modification to the FRL instrument. The positive towards advertising FRL dimension was modified to examine many kinds of information search including the internet, TV, magazines, and other people. This new dimension, which was designated as being open to additional information, proved to be very robust and reliable in finding differences in consumer choice behaviour. Active additional information search was linked to adventurous and snacking food-related lifestyles. The results of this study support the previous knowledge that consumers expect to get many benefits simultaneously when they buy food products. This study brought detailed information about the benefits sought, the combination of benefits differing between products and between respondents. Household economy, pleasure and quality were emphasized with the choice of lettuce. Quality was the most significant benefit in choosing mincemeat, but health related benefits were often evaluated as well. The dominant benefits linked to savoury sauce were household economic benefits, expected pleasurable experiences, and a lift in self-respect. The choice of goat cheese appeared not to be an economic decision, self-respect, pleasure, and quality being included in the choice criteria. In choosing pudding, the respondents considered the well-being of family members, and indulged their family members or themselves.