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.

Kaukainen rakkaus : Saavuttamattomuuden semantiikka Kaija Saariahon oopperassa

L Amour de loin: The semantics of the unattainable in Kaija Saariaho s opera Kaija Saariaho (born 1952) is one of the most internationally successful Finnish composers there has ever been. Her first opera L Amour de loin (Love from afar, 1999-2000) has been staged all over the world and has won a number of important prizes. The libretto written for L Amour de loin by Amin Malouf (born 1949) sets the work firmly in the culture of courtly love and the troubadours, which flourished in Occitania in the South of France during the Middle Ages. The male lead in the opera is the troubadour Jaufré Rudel, who lived in the twelfth century and is known to have taken part in the Second Crusade in 1147-1148. This doctoral thesis L Amour de loin: The semantics of the unattainable in Kaija Saariaho s opera, which comes within the field of musicology and opera research, examines the dimensions of meaning contained in Kaija Saariaho s opera L Amour de loin. This hermeneutic-semiotic study is the first doctoral thesis dealing with Saariaho to be completed at the University of Helsinki. It is also the first thesis-level study of Saariaho s opera to be completed anywhere in the world. The study focuses on the libretto and music of the opera, that is to say the dramatic text (L Amour de loin 1980), and examines on the one hand the dimensions of meaning produced by the dramatic text and on the other, the way in which they fix the dramatic text in a historical and cultural context. Thus the study helps to answer questions about the dimensions of meaning contained in the dramatic text of the opera and how they can be interpreted. The most important procedural viewpoint is Lawrence Kramer s hermeneutic window (1990), supplemented by Raymond Monelle s semiotic theory of musical topics (2000, 2006) and the philosophical concept of Emmanuel Levinas (1996, 2002) in which the latter acts as an instrument for semantic interpretation to build up an analysis. The analytical section of the study is built around the three characters in the opera, Jaufré Rudel, Clémence the Countess of Tripoli, and the Pilgrim. The study shows that the music of Saariaho, who belongs to the third generation of Finnish modernists, has become distanced from the post-serial aesthetic towards a more diatonic form of expression. There is diatonicity, for instance, in the sonorous individuality of the male lead, which is based on the actual melodies of the historical Jaufré Rudel. The use of outside material in this context is exceptional in the work of Saariaho. At the same time, Saariaho s opera contains a wealth of expressive devices she has used in her earlier work. It became apparent during the study that, as a piece of music, L Amour de loin is a many layered and multi-dimensional work that does not unambiguously represent any single stylistic trend or aesthetic. Despite the composer s post-serial background and its abrasive relationship with opera, L Amour de loin is firmly attached to the tradition of western opera. The analysis based on the theory of musical topics that was carried out in the study, shows that topics referring to death and resurrection, used in opera since the seventeenth century, appear in L Amour de loin. The troubadour topic, mainly identified with the harp, also emerges in the work. The study also shows that the work is firmly attached to the tradition of western opera in other aspects, too, such as the travesti or trouser role played by the Pilgrim, and the idea of deus ex machina derived from Ancient Greek theatre. The study shows that the concept of love based on the medieval practices of courtly love, and the associated longing for another defined by almost 1,000 years of western culture, are both manifested in the semantics of Kaija Saariaho s opera which takes its place in the contemporary music genre.

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.

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.

On the fundamentals of coherence theory

In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.