京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18447号 / 理博第4007号 / 新制||理||1578(附属図書館) / 31325 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 畑 浩之, 教授 川合 光, 准教授 市川 温子 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The goal of this thesis is to investigate a conjecture about Mirror Symmetry for Landau Ginzburg (LG) models with non-abelian gauge groups. The conjecture predicts that the LG A-model for a polynomial-group pair $(W,G)$ is equivalent to the LG B-model for the dual pair $(W^*, G^*)$. In particular, the A-model and B-model include the construction of a Frobenius algebra. The LG mirror symmetry conjecture predicts that the A-model Frobenius algebra for $(W,G)$ will be isomorphic to the B-model Frobenius algebra for the dual pair $(W^*,G^*)$. Part of the conjecture includes a rule describing how to construct the dual pair. Until now, no examples of this phenomenon have been verified. In this thesis we will verify the conjecture for the polynomial $W(x_1,x_2,x_3,x_4) = x_1^4+x_2^4+x_3^4+x_4^4$ with a maximal admissible non-abelian group. I present a supplementary guide along with a worked example to compute the state spaces of each of the A and B models with non-abelian groups. This includes formalizing G-actions to take invariants, computing each state space, formalizing the product on each state space, and as the main result, showing there indeed exists an isomorphism of Graded Frobenius Algebras between the LG A-model and dual LG B-model.

In recent years, consumers have witnessed a technological revolution that has delivered more-realistic experiences in their own homes. Expanding technologies have provided larger displays with higher resolutions, faster refresh rates, and stereoscopic capabilities. These advances have increased the level of display fidelity—the objective degree of exactness with which real-world sensory stimuli are reproduced by a display system. Similarly, the latest generation of video game systems (e.g., Nintendo Wii and Xbox Kinect) with their natural, gesture-based interactions have delivered increased levels of interaction fidelity—the objective degree of exactness with which real-world interactions can be reproduced in an interactive system. Though this technological revolution has provided more realistic experiences, it is not completely clear how increased display fidelity and interaction fidelity impact the user experience because the effects of increasing fidelity to the real world have not been empirically established. The goal of this dissertation is to provide a better understanding of the effects of both display fidelity and interaction fidelity on the user experience. For the context of our research, we chose virtual reality (VR) games because immersive VR allows for high levels of fidelity to be achieved while games usually involve complex, performance-intensive tasks. In regard to the user experience, we were concerned with objective performance metrics and subjective responses such as presence, engagement, perceived usability, and overall preferences. We conducted five systematically controlled studies that evaluated display and interaction fidelity at contrasting levels in order to gain a better understanding of their effects. In our first study, which involved a 3D object manipulation game within a three-sided CAVE, we found that stereoscopy and the total size of the visual field surrounding the user (i.e., field of regard or FOR) did not have a significant effect on manipulation times but two high-fidelity interaction techniques based on six degrees-of-freedom (DOF) input outperformed a low-fidelity technique based on keyboard and mouse input. In our second study, which involved a racing game on a commercial game console, we solely investigated interaction fidelity and found that two low-fidelity steering techniques based on 2D joystick input outperformed two high-fidelity steering techniques based on 3D accelerometer data in terms of lap times and driving errors. Our final three studies involved a first-person shooter (FPS) game implemented within a six-sided CAVE. In the first of these FPS studies, we evaluated display fidelity and interaction fidelity independently, at extremely high and low levels, and found that both significantly affected strategy, performance, presence, engagement, and perceived usability. In particular, performance results were strongly in favor of two conditions: low-display, low-interaction fidelity (representative of desktop FPS games) and high-display, high-interaction fidelity (similar to the real world). In the second FPS study, we investigated the effects of FOR and pointing fidelity on the subtasks of searching, aiming, and firing. We found that increased FOR affords faster searching and that high-fidelity pointing based on 6-DOF input provided faster aiming than low-fidelity mouse pointing and a mid-fidelity mouse technique based on the heading of the user. In the third FPS study, we investigated the effects of FOR and locomotion fidelity on the subtasks of long-distance navigation and maneuvering. Our results indicated that increased FOR increased perceived usability but had no significant effect on actual performance while low-fidelity keyboard-based locomotion outperformed our high-fidelity locomotion technique developed for our original FPS study. The results of our five studies show that increasing display fidelity tends to have a positive correlation to user performance, especially for some components such as FOR. Contrastingly, our results have indicated that interaction fidelity has a non-linear correlation to user performance with users performing better with "traditionalThe results of our five studies show that increasing display fidelity tends to have a positive correlation to user performance, especially for some components such as FOR. Contrastingly, our results have indicated that interaction fidelity has a non-linear correlation to user performance with users performing better with "traditional", extremely low-fidelity techniques and "natural", extremely high-fidelity techniques while performing worse with mid-fidelity interaction techniques. These correlations demonstrate that the display fidelity and interaction fidelity continua appear to have differing effects on the user experience for VR games. In addition to learning more about the effects of display fidelity and interaction fidelity, we have also developed the Framework for Interaction Fidelity Analysis (FIFA) for comparing interaction techniques to their real-world counterparts. There are three primary factors of concern within FIFA: biomechanical symmetry, control symmetry, and system appropriateness. Biomechanical symmetry involves the comparison of the kinematic, kinetic, and anthropometric aspects of two interactions. Control symmetry compares the dimensional, transfer function, and termination characteristics of two interactions. System appropriateness is concerned with how well a VR system matches the interaction space and objects of the real-world task (e.g., a driving simulator is more appropriate than a 2D joystick for a steering task). Although consumers have witnessed a technological revolution geared towards more realistic experiences in recent years, we have demonstrated with this research that there is still much to be learned about the effects of increasing a system's fidelity to the real world. The results of our studies show that the levels of display and interaction fidelity are significant factors in determining performance, presence, engagement, and usability. / Ph. D.

We present a calculation of vector and axial-vector form factors for each of the octet hyperon semi-leptonic transition matrix elements by using the techniques of lattice QCD where simulations were performed with Nf = 2 + 1 flavours of dynamical O(a)-improved Wilson fermions. We also study the electromagnetic form factors, axial charges and other properties of octet baryons. Errors due to extrapolation to zero transferred momentum are reduced by applying a twist to the boundary conditions on the lattice. Our form factor results compare favourably with experiment and other lattice QCD determinations. By considering an expansion about the SU(3)-flavour symmetric limit we seek to investigate and quantify the symmetry breaking effects in these matrix elements due to the mass splitting between the strange and light quarks. We find good agreement with the Ademollo-Gatto theorem for the vector form factor, a measurable amount of breaking in the axial-vector form factor and significant effects in the weak magnetism form factor. Knowledge of the parameterisation of SU(3)-flavour symmetry breaking allows for a series of constrained fits to be made to the form factor results which are used to arrive at a 'baryonic' estimation of the Cabibbo-Kobayashi-Maskawa matrix element |Vus|.

There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

Variable symmetries in constraint satisfaction problems can be broken by adding lexicographic ordering constraints. Existing general methods of generating such sets of ordering constraints can produce a huge number of additional constraints. This adds an unacceptable overhead to the solving process. Methods exist by which this large set of constraints can be reduced to a much smaller set automatically, but their application is also prohibitively costly. In contrast, this thesis takes a bottom up approach to generating symmetry breaking constraints. This will involve examining some commonly-occurring families of mathematical groups and deriving a general formula to produce a minimal set of ordering constraints which are sufficient to break all of the symmetry that each group describes. In some cases it is known that there exists no manageable sized sets of constraints to break all symmetries. One example of this occurs with matrix row and column symmetries. In such cases, incomplete symmetry breaking has been used to great effect. Double lex is a commonly used incomplete symmetry breaking technique for row and column symmetries. This thesis also describes another similar method which compares favourably to double lex. The general formulae investigated are used as building blocks to generate small sets of ordering constraints for more complex groups, constructed by combining smaller groups. Through the utilisation of graph automorphism tools and the groups and permutations software GAP we provide a method of defining variable symmetries in a problem as a group. Where this group can be described as the product of smaller groups, with known general formulae, we can construct a minimal set of ordering constraints for that problem automatically. In summary, this thesis provides the theoretical background necessary to apply efficient static symmetry breaking to constraint satisfaction problems. It also goes further, describing how this process can be automated to remove the necessity of having an expert CP practitioner, thus opening the field to a larger number of potential users.

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At the dawn of the Large Hadron Collider era, the Brout-Englert-Higgs mechanism remains the most appealing theoretical explanation of the electroweak symmetry breaking, despite the fact that the associated fundamental scalar boson has escaped any direct detection attempt. In this thesis, we consider a particular extension of the minimal Brout-Englert-Higgs scalar sector implemented in the Standard Model of strong and electroweak interactions. This extension, which is a specific, "twisted", realisation of the generic two-Higgs-doublet model, is motivated by a relative phase in the definition of the phenomenologically successful CP and custodial symmetries. Considering extensively various theoretical, indirect and direct constraints, this model appears as a viable alternative to more conventional scenarios like supersymmetric models, and gives grounds to largely unexplored possibilities of exotic scalar signatures at present and future collider experiments.

In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices. The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.

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