Neste trabalho empregamos a técnica de BFV para quantizar uma teoria com simetria de gauge SP(2;R). Para isso em primeiro lugar, analisamos o critério de admissibilidade de Govaerts para as condições de gauge para a teoria da partícula relativística, cujo propagador é calculado nos gauges covariante, canônico e do cone de luz por meio da discretização da integral de trajetória e esta mostra que a ação discretizada perde a invariância por transforma ções de BRST; e para restaurar sua invariância é necessário modificar as transformaçoes de BRST. Em segundo lugar, aplicamos a técnica de BFV para uma teoria com dois tempos e simetria de gauge SP(2;R), em seguida, analisamos o efeito da discretização e mostramos que a ação discretizada perde a invariância por transformações de BRST. Neste caso, as modificações necessárias incluem termos de ordem N nas transformações de BRST e estas passam a ser nilpotentes apenas on-shell. Ao fixarmos um tempo físico de duas formas diferentes obtivemos o propagador de uma partícula relativística em d dimensões e de um oscilador harmônico invertido em d - 2 dimensões espaciais. / In this work we employ the BFV technique to quantize a theory with gauge symmetry Sp(2;R). First, we analyze the admissibility criterion of Govaerts for gauge conditions on the theory of a relativistic particle. The propagator for the relativistic particle is calculated in the covariant, canonical and light cone gauges. The discretization of the path integral shows that the discretized action looses invariance by the BRST transformations. To restore the invariance it is necessary to include modified transformations. Secondly, we apply the BFV technique to a theory with two times and gauge symmetry Sp(2;R). We analyze the effect of discretization and show that the discretized action looses the BRST invariance. In this case, it is necessary to change the transformations including terms of order N , which become nilpotent only on-shell. Fixing the physical time in two different ways we get the propagator for a relativistic particle in d dimensions and for an inverted harmonic oscillator in d - 2 spatial dimensions.

In this thesis, topologically massive Yang-Mills theory is studied in the framework of geometric quantization. This theory has a mass gap that is proportional to the topological mass m. Thus, Yang-Mills contribution decays exponentially at very large distances compared to 1/m, leaving a pure Chern-Simons theory with level number k. The focus of this research is the near Chern-Simons limit of the theory, where the distance is large enough to give an almost topological theory, with a small contribution from the Yang-Mills term. It is shown that this almost topological theory consists of two copies of Chern-Simons with level number k/2, very similar to the Chern-Simons splitting of topologically massive AdS gravity model. As m approaches to infinity, the split parts add up to give the original Chern-Simons term with level k. Also, gauge invariance of the split CS theories is discussed for odd values of k. Furthermore, a relation between the observables of topologically massive Yang-Mills theory and Chern-Simons theory is obtained. It is shown that one of the two split Chern-Simons pieces is associated with Wilson loops while the other with 't Hooft loops. This allows one to use skein relations to calculate topologically massive Yang-Mills theory observables in the near Chern-Simons limit. Finally, motivated with the topologically massive AdS gravity model, Chern-Simons splitting concept is extended to pure Yang-Mills theory at large distances. It is shown that pure Yang-Mills theory acts like two Chern-Simons theories with level numbers k/2 and -k/2 at large scales. At very large scales, these two terms cancel to make the theory trivial, as required by the existence of a mass gap.

Le but de cette thèse est d'étudier quelques aspects algébriques du problème de quantification par déformation. On considère d'une part la formalité dans le cas des algèbres libres et de l'algèbre de Lie so(3), et on s'intéresse d'autre part à la quantification par déformation pour des structures Hom-algébriques. Suivant le résultat de formalité de Kontsevich en 1997 pour les algèbres symétriques, on étudie dans la première partie de cette thèse les algèbres libres, qui sont un cas particulier d'algèbres enveloppantes, et on montre qu'il n'y a pas formalité en général, sauf dans les cas triviaux. On montre aussi qu'il n'y a pas formalité pour l'algèbre de Lie so(3). Les techniques utilisées sont de type homologiques. On calcule la cohomologie de ces algèbres et on procède à la construction du L-infini-quasi-isomorphisme entre l'algèbre de Lie différentielle graduée des cochaînes de Hochschild munie du crochet de Gerstenhaber et l'algèbre de la cohomologie munie du crochet de Schouten. Dans la seconde partie de ce travail, on utilise un principe de déformation par twist pour les structures Hom-algébriques, pour construire de nouvelles structures de même type, ou encore pour déformer une structure classique en une Hom-structure correspondante à l'aide d'un morphisme d'algèbres. En particulier, on applique ce procédé aux structures de Poisson et aux star-produits de Moyal-Weyl. Par ailleurs, on établit une correspondance entre les algèbres enveloppantes d'algèbres Hom-Lie possédant une structure Hom-coPoisson et les bigèbres Hom-Lie. / This thesis aims to study some algebraic aspects of the deformation quantization problem. On one hand, we consider formality for free algebras and the Lie algebra so(3), and on the other hand we study deformation quantization for Hom-algebraic structures. Following Kontsevich's formality result in 1997 for symmetric algebras, we study in the first part free algebras, which are a particular case of envelopping algebras, and show that there is no formality, except for the trivial cases. We also show that there is no formality for the Lie algebra so(3). The tools used are homological ones. We compute the cohomology of these algebras and proceed to the construction of the L-infinity-quasi-isomorphism between the differential graded Lie algebra of the Hochschild cochains endowed with the Gerstenhaber bracket and the cohomology algebra endowed with the Schouten bracket. In the second part of this work, we use a principle of deformation by twist for Hom-algebraic structures, to construct new structures of the same type, or to deform a classical structure in the corresponding Hom-structure using an algebra morphism. In particular, we apply this method to Poisson structures and Moyal-Weyl star-products. Besides, we establish a correspondance between enveloping algebras of Hom-Lie algebras endowed with a Hom-coPoisson structure and Hom-Lie bialgebras.

In this dissertation, we study properties of quantum interaction phenomena in two-dimensional (2D) and one-dimensional (1D) electronic systems in p-GaAs micro- and nano-scale devices. We present low-temperature magneto-transport data from three forms of low-dimensional systems 1) 2D hole systems: in order to study interaction contributions to the metallic behavior of 2D systems 2) Bilayer hole systems: in order to study the many body, bilayer quantum Hall state at nu = 1 3) 1D hole systems: for the study of the anomalous conductance plateau G = 0.7 ???? 2e2/h The work is divided into five experimental studies aimed at either directly exploring the properties of the above three interaction phenomena or the development of novel device structures that exploit the strong particle-particle interactions found in p-GaAs for the study of many body phenomena. Firstly, we demonstrate a novel semiconductor-insulator-semiconductor field effect transistor (SISFET), designed specifically to induced 2D hole systems at a ????normal???? AlGaAs-on-GaAs heterojunction. The novel SISFETs feature in our studies of the metallic behavior in 2D systems in which we examine temperature corrections to ????xx(T) and ????xy(T) in short- and long-range disorder potentials. Next, we shift focus to bilayer hole systems and the many body quantum Hall states that form a nu = 1 in the presence of strong interlayer interactions. We explore the evolution of this quantum Hall state as the relative densities in the layers is imbalanced while the total density is kept constant. Finally, we demonstrate a novel p-type quantum point contact device that produce the most stable and robust current quantization in a p-type 1D systems to date, allowing us to observed for the first time the 0.7 structure in a p-type device.

<p>We study the spin polarization and conductance in infinitely long quasi one-dimensionalquantum wires under various conditions in an attempt to reproduce and to explain some of theanomalous conductance features as seen in various experiments. In order to accomplish thistask we create an idealized model of a quantum wire in a split-gate semiconductorheterostructure and we perform self-consistent Hartree-Fock calculations to determine theelectron occupation and spin polarization. Based on those results we calculate the currentthrough the wire as well as the direct and differential conductances. In the frame of theproposed model the results show a high degree of similarity to some of the experimentallyobserved conductance features, particularly the 0.25- and 0.85-plateaus. These results lead usto the conclusion that those conductance anomalies are in fact caused by the electronsspontaneously polarizing due to electron-electron interactions when an applied potentialdrives a current through the wire.</p>

As Moore���s Law continues to give rise to ever shrinking channel lengths, circuits are becoming more digital and ever increasingly faster. Generating high frequency clocks in such scaled processes is becoming a tough challenge. Digital phase locked loops (DPLLs) are being explored as an alternative to conventional analog PLLs but suffer from issues such as low bandwidth and higher quantization noise. A digital multiplying delay locked loop (DMDLL) is proposed which aims at leveraging the benefit of high bandwidth of DLL while at the same time achieving the frequency multiplication property of PLL. It also offers the benefits of easier portability across process and occupies lesser area. The proposed DMDLL uses a simple flip-flop as 1-bit TDC (Time Digital Converter) for Phase Detector (PD). A digital accumulator acts as integrator for loop filter while a ��-�� DAC in combination with a VCO acts like a DCO. A carefully designed select logic in conjunction with a MUX achieves frequency multiplication. The proposed digital MDLL is taped out in 130nm process and tested to obtain 1.4GHz output frequency with 1.6ps RMS jitter, 17ps peak-to-peak jitter and -50dbC/Hz reference spurs. / Graduation date: 2012

The work is divided into three main parts. In a first time (chapter 1) we define a “BTZ” black hole in anti de Sitter space in any dimension. That will be done by means of group theoretical and symmetric spaces considerations. A physical “good domain” is identified as an open orbit of a subgroup of the isometry group of anti de Sitter. Then (chapter 2) we show that the open orbit is in fact isomorphic to a group (we introduce the notion of globally group type manifold) for which a quantization exists. The quantization of the black hole is performed and its Dirac operator is computed. The third part (appendix A and B) exposes some previously known results. Appendix A is given in a pedagogical purpose: it exposes generalities about deformation quantization and careful examples with SL(2,R), and split extensions of Heisenberg algebras. Appendix B is devoted to some classical results about homogeneous spaces and Iwasawa decompositions. Explicit decompositions are given for every algebra that will be used in the thesis. It serves to make the whole text more self contained and to fix notations. Basics of quantization by group action are given in appendix A.4. One more chapter is inserted (chapter 3). It contains two small results which have no true interest by themselves but which raise questions and call for further development. We discuss a product on the half-plane or, equivalently, on the Iwasawa subgroup of SL(2,R), due to A. Unterberger. We show that the quantization by group action machinery can be applied to this product in order to deform the dual of the Lie algebra of that Iwasawa subgroup. Although this result seems promising, we show by two examples that the product is not universal in the sense that even the product of compactly supported functions cannot be defined on AdS2 by the quantization induced by Unterberger's product. Then we show that the Iwasawa subgroup of SO(2,n) (i.e. the group which defines the singularity) is a symplectic split extension of the Iwasawa subgroup of SU(1,1) by the Iwasawa subgroup of SU(1,n). A quantization of the two latter groups being known, a quantization of SO(2,n) is in principle possible using an extension lemma. Properties of this product and the resulting quantization of AdSl were not investigated because we found a more economical way to quantize AdS4 .

A light stripe vision system is used to measure the location of polyhedral features of parts from a single frame of video camera output. Issues such as accuracy in locating the line segments of intersection in the image and combining redundant information from multiple measurements and multiple sources are addressed. In 2.5 seconds, a prototype sensor was capable of locating a two inch cube to an accuracy (one standard deviation) of .002 inches (.055 mm) in translation and .1 degrees (.0015 radians) in rotation. When integrated with a manipulator, the system was capable of performing high precision assembly tasks.

Quantization of multimodal vector data in Realtime Interactive Communication Networks (RICNs) associated with application areas such as speech, video, audio, and haptic signals introduces a set of unique challenges. In particular, achieving the necessary distortion performance with minimum rate while maintaining low end-to-end delay and handling packet losses is of paramount importance. This dissertation presents vector quantization schemes which aim to satisfy these important requirements based on two source coding paradigms; 1) Predictive coding 2) Distributed source coding. Gaussian Mixture Models (GMMs) can be used to model any probability density function (pdf) with an arbitrarily small error given a sufficient number of mixture components. Hence, Gaussian Mixture Models can be effectively used to model the underlying pdfs of a variety of data in RICN applications. In this dissertation, first we present Gaussian Mixture Models Kalman predictive coding, which uses transform domain predictive GMM quantization techniques with Kalman filtering principles. In particular, we show how suitable modeling of quantization noise leads to a signal-adaptive GMM Kalman predictive coder that provides improved coding performance. Moreover, we demonstrate how running a GMM Kalman predictive coder to convergence can be used to design a stationary GMM Kalman predictive coding system which provides improved coding of GMM vector data but now with only a modest increase in run-time complexity over the baseline. Next, we address the issues of packet loss in the networks using GMM Kalman predictive coding principles. In particular, we show how an initial GMM Kalman predictive coder can be utilized to obtain a robust GMM predictive coder specifically designed to operate in packet loss. We demonstrate how one can define sets of encoding and decoding modes, and design special Kalman encoding and decoding gains for each mode. With this framework, GMM predictive coding design can be viewed as determining the special Kalman gains that minimize the expected mean squared error at the decoder in packet loss conditions. Finally, we present analytical techniques for modeling, analyzing and designing Wyner-Ziv(WZ) quantizers for Distributed Source Coding for jointly Gaussian vector data with imperfect side information. In most of the DSC implementations, the side information is not explicitly available in the decoder. Thus, almost all of the practical implementations obtain the side information from the previously decoded frames. Due to model imperfections, packet losses, previous decoding errors, and quantization noise, the available side information is usually noisy. However, the design of Wyner-Ziv quantizers for imperfect side information has not been widely addressed in the DSC literature. The analytical techniques presented in this dissertation explicitly assume the existence of imperfect side information in the decoder. Furthermore, we demonstrate how the design problem for vector data can be decomposed into independent scalar design subproblems. Then, we present the analytical techniques to compute the optimum step size and bit allocation for each scalar quantizer such that the decoder's expected vector Mean Squared Error(MSE) is minimized. The simulation results verify that the predicted MSE based on the presented analytical techniques closely follow the simulation results.

One deals in this work with the existence and the uniqueness of natural projectively equivariant quantizations by means of the theory of Cartan connections. One shows that a natural projectively equivariant quantization exists for differential operators acting between $lambda$ and $mu$-densities if and only if the corresponding $sl(m+1,mathbb{R})$-equivariant quantization on $mathbb{R}^{m}$ exists. With this end in view, one writes the quantization by means of a formula in terms of the normal Cartan connection associated to the projective structure of a connection. One deduces next an explicit formula for the natural projectively equivariant quantization. One shows the non-uniqueness of such a quantization by means of the curvature of the normal Cartan connection. Finally, one shows the existence of natural and projectively equivariant quantizations for differential operators acting between sections of other natural fiber bundles transposing the method used in $mathbb{R}^{m}$ to analyse the existence of $sl(m+1,mathbb{R})$-equivariant quantizations, this method being linked to the Casimir operator./ On traite dans cet ouvrage de l'existence et de l'unicité de quantifications naturelles projectivement équivariantes au moyen de la théorie des connexions de Cartan. On démontre qu'une quantification naturelle projectivement équivariante existe pour des opérateurs différentiels agissant entre $lambda$ et $mu$-densités si et seulement si la quantification $sl(m+1,mathbb{R})$- équivariante correspondante sur $mathbb{R}^{m}$ existe. Pour cela, on exprime la quantification au moyen d'une formule en termes de la connexion de Cartan normale associée à la structure projective d'une connexion. On en déduit ensuite une formule explicite pour la quantification naturelle projectivement invariante. On démontre après la non-unicité d'une telle quantification par le biais de la courbure de la connexion de Cartan normale. Enfin, on démontre l'existence de quantifications naturelles projectivement équivariantes pour des opérateurs différentiels agissant entre sections d'autres fibrés naturels en transposant la méthode utilisée dans $mathbb{R}^{m}$ pour analyser l'existence de quantifications $sl(m+1,mathbb{R})$-équivariantes, méthode liée à l'opérateur de Casimir.