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.

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.

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.

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.

The Problem of Implementation and its Relation to the Philosophy of Cognitive Science

According to certain arguments, computation is observer-relative either in the sense that many physical systems implement many computations (Hilary Putnam), or in the sense that almost all physical systems implement all computations (John Searle). If sound, these arguments have a potentially devastating consequence for the computational theory of mind: if arbitrary physical systems can be seen to implement arbitrary computations, the notion of computation seems to lose all explanatory power as far as brains and minds are concerned. David Chalmers and B. Jack Copeland have attempted to counter these relativist arguments by placing certain constraints on the definition of implementation. In this thesis, I examine their proposals and find both wanting in some respects. During the course of this examination, I give a formal definition of the class of combinatorial-state automata , upon which Chalmers s account of implementation is based. I show that this definition implies two theorems (one an observation due to Curtis Brown) concerning the computational power of combinatorial-state automata, theorems which speak against founding the theory of implementation upon this formalism. Toward the end of the thesis, I sketch a definition of the implementation of Turing machines in dynamical systems, and offer this as an alternative to Chalmers s and Copeland s accounts of implementation. I demonstrate that the definition does not imply Searle s claim for the universal implementation of computations. However, the definition may support claims that are weaker than Searle s, yet still troubling to the computationalist. There remains a kernel of relativity in implementation at any rate, since the interpretation of physical systems seems itself to be an observer-relative matter, to some degree at least. This observation helps clarify the role the notion of computation can play in cognitive science. Specifically, I will argue that the notion should be conceived as an instrumental rather than as a fundamental or foundational one.

Sensemaking in the Third Space - Essays on French-Finnish Bicultural Experiences in Organizations and Their Narratives (summary section only)

Research on cross-cultural and intercultural aspects in organizations has been traditionally conducted from an objectivist, functionalist perspective, with culture treated as an independent variable, and often the key explanatory factor. In order to do justice to the ontological relativity of the phenomena studied, more subjectivist research on intercultural interactions, and especially on their relationships with the dynamics of cultural identity construction, is needed. The present research seeks to address this gap by focusing on bicultural interactions in organizations, as they are experienced by the involved individuals. It is argued that such bicultural situations see the emergence of a space of hybridity, which is here called a ‘third space’, and which can be understood as providing ‘occasions for sensemaking’: it is this individual sensemaking that is of particular interest in the empirical narrative study. A first overall aim of the study is to reach an understanding of the dynamics of bicultural interactions in organizations; an understanding not only of the potential for learning and emancipatory sensemaking, but also of the possibility of conflict and alienatory ordering (this is mainly addressed in the theoretical essays 1 and 2). Further, a second overall aim of the study is to analyze the reflexive identity construction of four young French expatriates involved in such bicultural interactions in organizations in Finland, in order to examine the extent to which their expatriation experiences have allowed for an emancipatory opportunity in their cases (in essays 3 and 4). The primary theoretical contribution in this study lies in its new articulation of the dynamics of bicultural interactions in organizations. The ways in which the empirical material is analyzed bring about methodological contributions: since the expatriates’ accounts are bound to be some kind of construction, the analysis is made from angles that point to how the self-narratives construct reality. There are two such angles here: a ‘performative’ one and a ‘spatial’ one. The most important empirical contributions lie in the analysis of, on the one hand, the alternative uses that the young expatriates made of the notion of ‘national culture’ in their self-narratives, and, on the other hand, their ‘narrative practices of the third space’: their politics of escape or stabilization, their exploration of space or search for place, their emancipation from their origin or return to home as only horizon.