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.

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.

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.

A Historical Approach to Children s Physics Education : Modelling of DC-circuit Phenomena in a Small Group

This three-phase design research describes the modelling processes for DC-circuit phenomena. The first phase presents an analysis of the development of the DC-circuit historical models in the context of constructing Volta s pile at the turn of the 18th century. The second phase involves the designing of a teaching experiment for comprehensive school third graders. Among other considerations, the design work utilises the results of the first phase and research literature of pupils mental models for DC-circuit phenomena. The third phase of the research was concerned with the realisation of the planned teaching experiment. The aim of this phase was to study the development of the external representations of DC-circuit phenomena in a small group of third graders. The aim of the study has been to search for new ways to guide pupils to learn DC-circuit phenomena while emphasing understanding at the qualitative level. Thus, electricity, which has been perceived as a difficult and abstract subject, could be learnt more comprehensively. Especially, the research of younger pupils learning of electricity concepts has not been of great interest at the international level, although DC-circuit phenomena are also taught in the lower classes of comprehensive schools. The results of this study are important, because there has tended to be more teaching of natural sciences in the lower classes of comprehensive schools, and attempts are being made to develop this trend in Finland. In the theoretical part of the research an Experimental-centred representation approach, which emphasises the role of experimentalism in the development of pupil s representations, is created. According to this approach learning at the qualitative level consists of empirical operations like experimenting, observations, perception, and prequantification of nature phenomena, and modelling operations like explaining and reasoning. Besides planning teaching, the new approach can be used as an analysis tool in describing both historical modelling and the development of pupils representations. In the first phase of the study, the research question was: How did the historical models of DC-circuit phenomena develop in Volta s time? The analysis uncovered three qualitative historical models associated with the historical concept formation process. The models include conceptions of the electric circuit as a scene in the DC-circuit phenomena, the comparative electric-current phenomenon as a cause of different observable effect phenomena, and the strength of the battery as a cause of the electric-current phenomenon. These models describe the concept formation process and its phases in Volta s time. The models are portrayed in the analysis using fragments of the models, where observation-based fragments and theoretical fragements are distinguished from each other. The results emphasise the significance of the qualitative concept formation and the meaning of language in the historical modelling of DC-circuit phenomena. For this reason these viewpoints are stressed in planning the teaching experiment in the second phase of the research. In addition, the design process utilised the experimentation behind the historical models of DC-circuit phenomena In the third phase of the study the research question is as follows: How will the small group s external representations of DC-circuit phenomena develop during the teaching experiment? The main question is divided into the following two sub questions: What kind of talk exists in the small group s learning? What kinds of external representations for DC-circuit phenomena exist in the small group discourse during the teaching experiment? The analysis revealed that the teaching experiment of the small group succeeded in its aim to activate talk in the small group. The designed connection cards proved especially successful in activating talk. The connection cards are cards that represent the components of the electric circuit. In the teaching experiment the pupils constructed different connections with the connection cards and discussed, what kinds of DC-circuit phenomena would take place in the corresponding real connections. The talk of the small group was analysed by comparing two situations, firstly, when the small group discussed using connections made with the connection cards and secondly with the same connections using real components. According to the results the talk of the small group included more higher-order thinking when using the connection cards than with similar real components. In order to answer the second sub question concerning the small group s external representations that appeared in the talk during the teaching experiment; student talk was visualised by the fragment maps which incorporate the electric circuit, the electric current and the source voltage. The fragment maps represent the gradual development of the external representations of DC-circuit phenomena in the small group during the teaching experiment. The results of the study challenge the results of previous research into the abstractness and difficulty of electricity concepts. According to this research, the external representations of DC-circuit phenomena clearly developed in the small group of third graders. Furthermore, the fragment maps uncover that although the theoretical explanations of DC-circuit phenomena, which have been obtained as results of typical mental model studies, remain undeveloped, learning at the qualitative level of understanding does take place.

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.

Studies of electronic structure by x-ray Raman and emission spectroscopy: applications to MgB2 superconductors and high pressure physics

X-ray Raman scattering and x-ray emission spectroscopies were used to study the electronic properties and phase transitions in several condensed matter systems. The experimental work, carried out at the European Synchrotron Radiation Facility, was complemented by theoretical calculations of the x-ray spectra and of the electronic structure. The electronic structure of MgB2 at the Fermi level is dominated by the boron σ and π bands. The high density of states provided by these bands is the key feature of the electronic structure contributing to the high critical temperature of superconductivity in MgB2. The electronic structure of MgB2 can be modified by atomic substitutions, which introduce extra electrons or holes into the bands. X ray Raman scattering was used to probe the interesting σ and π band hole states in pure and aluminum substituted MgB2. A method for determining the final state density of electron states from experimental x-ray Raman scattering spectra was examined and applied to the experimental data on both pure MgB2 and on Mg(0.83)Al(0.17)B2. The extracted final state density of electron states for the pure and aluminum substituted samples revealed clear substitution induced changes in the σ and π bands. The experimental work was supported by theoretical calculations of the electronic structure and x-ray Raman spectra. X-ray emission at the metal Kβ line was applied to the studies of pressure and temperature induced spin state transitions in transition metal oxides. The experimental studies were complemented by cluster multiplet calculations of the electronic structure and emission spectra. In LaCoO3 evidence for the appearance of an intermediate spin state was found and the presence of a pressure induced spin transition was confirmed. Pressure induced changes in the electronic structure of transition metal monoxides were studied experimentally and were analyzed using the cluster multiplet approach. The effects of hybridization, bandwidth and crystal field splitting in stabilizing the high pressure spin state were discussed. Emission spectroscopy at the Kβ line was also applied to FeCO3 and a pressure induced iron spin state transition was discovered.