The first goal of diploma thesis is to study the basic principles of video signal compression. Introduction to techniques used to reduce irrelevancy and redundancy in the video signal. The second goal is, on the basis of information about compression tools, implement the individual compression tools in the programming environment of Matlab and assemble simple model of the video codec. Diploma thesis contains a description of the three basic blocks, namely - interframe coding, intraframe coding and coding with variable length word - according the standard MPEG-2.

[EN] Multiple-Input Multiple-Output (MIMO) technology in Digital Terrestrial Television (DTT) networks has the potential to increase the spectral efficiency and improve network coverage to cope with the competition of limited spectrum use (e.g., assignment of digital dividend and spectrum demands of mobile broadband), the appearance of new high data rate services (e.g., ultra-high definition TV - UHDTV), and the ubiquity of the content (e.g., fixed, portable, and mobile). It is widely recognised that MIMO can provide multiple benefits such as additional receive power due to array gain, higher resilience against signal outages due to spatial diversity, and higher data rates due to the spatial multiplexing gain of the MIMO channel. These benefits can be achieved without additional transmit power nor additional bandwidth, but normally come at the expense of a higher system complexity at the transmitter and receiver ends. The final system performance gains due to the use of MIMO directly depend on physical characteristics of the propagation environment such as spatial correlation, antenna orientation, and/or power imbalances experienced at the transmit aerials. Additionally, due to complexity constraints and finite-precision arithmetic at the receivers, it is crucial for the overall system performance to carefully design specific signal processing algorithms. This dissertation focuses on transmit and received signal processing for DTT systems using MIMO-BICM (Bit-Interleaved Coded Modulation) without feedback channel to the transmitter from the receiver terminals. At the transmitter side, this thesis presents investigations on MIMO precoding in DTT systems to overcome system degradations due to different channel conditions. At the receiver side, the focus is given on design and evaluation of practical MIMO-BICM receivers based on quantized information and its impact in both the in-chip memory size and system performance. These investigations are carried within the standardization process of DVB-NGH (Digital Video Broadcasting - Next Generation Handheld) the handheld evolution of DVB-T2 (Terrestrial - Second Generation), and ATSC 3.0 (Advanced Television Systems Committee - Third Generation), which incorporate MIMO-BICM as key technology to overcome the Shannon limit of single antenna communications. Nonetheless, this dissertation employs a generic approach in the design, analysis and evaluations, hence, the results and ideas can be applied to other wireless broadcast communication systems using MIMO-BICM. / [ES] La tecnología de múltiples entradas y múltiples salidas (MIMO) en redes de Televisión Digital Terrestre (TDT) tiene el potencial de incrementar la eficiencia espectral y mejorar la cobertura de red para afrontar las demandas de uso del escaso espectro electromagnético (e.g., designación del dividendo digital y la demanda de espectro por parte de las redes de comunicaciones móviles), la aparición de nuevos contenidos de alta tasa de datos (e.g., ultra-high definition TV - UHDTV) y la ubicuidad del contenido (e.g., fijo, portable y móvil). Es ampliamente reconocido que MIMO puede proporcionar múltiples beneficios como: potencia recibida adicional gracias a las ganancias de array, mayor robustez contra desvanecimientos de la señal gracias a la diversidad espacial y mayores tasas de transmisión gracias a la ganancia por multiplexado del canal MIMO. Estos beneficios se pueden conseguir sin incrementar la potencia transmitida ni el ancho de banda, pero normalmente se obtienen a expensas de una mayor complejidad del sistema tanto en el transmisor como en el receptor. Las ganancias de rendimiento finales debido al uso de MIMO dependen directamente de las características físicas del entorno de propagación como: la correlación entre los canales espaciales, la orientación de las antenas y/o los desbalances de potencia sufridos en las antenas transmisoras. Adicionalmente, debido a restricciones en la complejidad y aritmética de precisión finita en los receptores, es fundamental para el rendimiento global del sistema un diseño cuidadoso de algoritmos específicos de procesado de señal. Esta tesis doctoral se centra en el procesado de señal, tanto en el transmisor como en el receptor, para sistemas TDT que implementan MIMO-BICM (Bit-Interleaved Coded Modulation) sin canal de retorno hacia el transmisor desde los receptores. En el transmisor esta tesis presenta investigaciones en precoding MIMO en sistemas TDT para superar las degradaciones del sistema debidas a diferentes condiciones del canal. En el receptor se presta especial atención al diseño y evaluación de receptores prácticos MIMO-BICM basados en información cuantificada y a su impacto tanto en la memoria del chip como en el rendimiento del sistema. Estas investigaciones se llevan a cabo en el contexto de estandarización de DVB-NGH (Digital Video Broadcasting - Next Generation Handheld), la evolución portátil de DVB-T2 (Second Generation Terrestrial), y ATSC 3.0 (Advanced Television Systems Commitee - Third Generation) que incorporan MIMO-BICM como clave tecnológica para superar el límite de Shannon para comunicaciones con una única antena. No obstante, esta tesis doctoral emplea un método genérico tanto para el diseño, análisis y evaluación, por lo que los resultados e ideas pueden ser aplicados a otros sistemas de comunicación inalámbricos que empleen MIMO-BICM. / [CA] La tecnologia de múltiples entrades i múltiples eixides (MIMO) en xarxes de Televisió Digital Terrestre (TDT) té el potencial d'incrementar l'eficiència espectral i millorar la cobertura de xarxa per a afrontar les demandes d'ús de l'escàs espectre electromagnètic (e.g., designació del dividend digital i la demanda d'espectre per part de les xarxes de comunicacions mòbils), l'aparició de nous continguts d'alta taxa de dades (e.g., ultra-high deffinition TV - UHDTV) i la ubiqüitat del contingut (e.g., fix, portàtil i mòbil). És àmpliament reconegut que MIMO pot proporcionar múltiples beneficis com: potència rebuda addicional gràcies als guanys de array, major robustesa contra esvaïments del senyal gràcies a la diversitat espacial i majors taxes de transmissió gràcies al guany per multiplexat del canal MIMO. Aquests beneficis es poden aconseguir sense incrementar la potència transmesa ni l'ample de banda, però normalment s'obtenen a costa d'una major complexitat del sistema tant en el transmissor com en el receptor. Els guanys de rendiment finals a causa de l'ús de MIMO depenen directament de les característiques físiques de l'entorn de propagació com: la correlació entre els canals espacials, l'orientació de les antenes, i/o els desequilibris de potència patits en les antenes transmissores. Addicionalment, a causa de restriccions en la complexitat i aritmètica de precisió finita en els receptors, és fonamental per al rendiment global del sistema un disseny acurat d'algorismes específics de processament de senyal. Aquesta tesi doctoral se centra en el processament de senyal tant en el transmissor com en el receptor per a sistemes TDT que implementen MIMO-BICM (Bit-Interleaved Coded Modulation) sense canal de tornada cap al transmissor des dels receptors. En el transmissor aquesta tesi presenta recerques en precoding MIMO en sistemes TDT per a superar les degradacions del sistema degudes a diferents condicions del canal. En el receptor es presta especial atenció al disseny i avaluació de receptors pràctics MIMO-BICM basats en informació quantificada i al seu impacte tant en la memòria del xip com en el rendiment del sistema. Aquestes recerques es duen a terme en el context d'estandardització de DVB-NGH (Digital Video Broadcasting - Next Generation Handheld), l'evolució portàtil de DVB-T2 (Second Generation Terrestrial), i ATSC 3.0 (Advanced Television Systems Commitee - Third Generation) que incorporen MIMO-BICM com a clau tecnològica per a superar el límit de Shannon per a comunicacions amb una única antena. No obstant açò, aquesta tesi doctoral empra un mètode genèric tant per al disseny, anàlisi i avaluació, per la qual cosa els resultats i idees poden ser aplicats a altres sistemes de comunicació sense fils que empren MIMO-BICM. / Vargas Paredero, DE. (2016). Transmit and Receive Signal Processing for MIMO Terrestrial Broadcast Systems [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/66081 / TESIS / Premios Extraordinarios de tesis doctorales

[pt] Com um número crescente de antenas em sistemas MIMO, o consumo de energia e os custos das interfaces de rádio correspondentes tornam-se relevantes. Nesse contexto, uma abordagem promissora é a utilização de conversores de dados de baixa resolução. Neste estudo, propomos dois novos pré-codificadores ótimos para a sinais de envelope constante e quantização de fase. O primeiro maximiza a distância mínima para o limite de decisão (MMDDT) nos receptores, enquanto o segundo minimiza o erro médio quadrático entre os símbolos dos usuários e o sinal de recepção. O design MMDDT apresetado nesse estudo é uma generalização de designs anteriores que baseiam-se em quantização de 1-bit. Além disso, ao contrário do projeto MMSE anterior que se baseia na resolução de 1-bit, a abordagem proposta emprega quantização de fase uniforme e a etapa de limite no método branch-and-bound é diferente em termos de considerar o relaxamento mais restritivo do problema não convexo, que é então utilizado para um design sub ótimo também. Além disso, três métodos diferentes de detecção suave e um esquema iterativo de detecção e decodificação que permite a utilização de codificação de canal em conjunto com pré-codificação de baixa resolução são propostos. Além de uma abordagem exata para calcular a informação extrínseca, duas aproximações com reduzida complexidade computacional são propostas. Os algoritmos propostos de pré-codificação branch-and-bound são superiores aos métodos existentes em termos de taxa de erro de bit. Resultados numéricos mostram que as abordagens propostas têm complexidade significativamente menor do que a busca exaustiva. Finalmente, os resultados baseados em um código de bloco LDPC indicam que os esquemas de processamento de recepção geram uma taxa de erro de bit menor em comparação com o projeto convencional. / [en] With an increasing number of antennas in multiple-input multiple-output (MIMO) systems, the energy consumption and costs of the corresponding front ends become relevant. In this context, a promising approach is the consideration of low-resolution data converters. In this study two novel optimal precoding branch-and-bound algorithms constrained to constant envelope signals and phase quantization are proposed. The first maximizes the minimum distance to the decision threshold (MMDDT) at the receivers, while the second minimizes the MSE between the users data symbols and the receive signal. This MMDDT design presented in this study is a generalization of prior designs that rely on 1-bit quantization. Moreover, unlike the prior MMSE design that relies on 1-bit resolution, the proposed MMSE approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. Moreover, three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding are proposed. Besides an exact approach for computing the extrinsic information, two approximations with reduced computational complexity are devised. The proposed branch-and-bound precoding algorithms are superior to the existing methods in terms of bit error rate. Numerical results show that the proposed approaches have significantly lower complexity than exhaustive search. Finally, results based on an LDPC block code indicate that the proposed receive processing schemes yield a lower bit-error-rate compared to the conventional design.

Emerging machine learning (ML) techniques are showing great potential in prediction performance. However, research and development is often conducted in an environment with extensive computational resources and blinded by prediction performance. In reality, computational resources might be contained on constrained hardware where energy and memory consumption must be restrained. Furthermore, shortages of sufficiently large datasets for ML is a frequent problem, combined with the cost of data retention. This generates a significant demand for sustainable ML. With sustainable ML, practitioners can train ML models on less data, which reduces memory and energy consumption during the training process. To explore solutions to these problems, this thesis dives into several techniques that have been introduced in the literature to achieve energy-savings when training machine learning models. These techniques include Quantization-Aware Training, Model Distillation, Quantized Distillation, Continual Learning and a deeper dive into Siamese Neural Networks (SNNs), one of the most promising techniques for sustainability. Empirical evaluations are conducted using several datasets to illustrate the potential of these techniques and their contribution to sustainable ML. The findings of this thesis show that the energy-saving techniques could be leveraged in some cases to make machine learning models more manageable and sustainable whilst not compromising significant model prediction performance. In addition, the deeper dive into SNNs shows that SNNs can outperform standard classification networks, under both the standard multi-class classification case and the Continual Learning case, whilst being trained on significantly less data. / Maskininlärning har i den senaste tidens forskning visat stor potential och hög precision inom klassificering. Forskning, som ofta bedrivs i en miljö med omfattande beräkningsresurser, kan lätt bli förblindad av precision. I verkligheten är ofta beräkningsresurser lokaliserade på hårdvara där energi- och minneskapacitet är begränsad. Ytterligare ett vanligt problem är att uppnå en tillräckligt stor datamängd för att uppnå önskvärd precision vid träning av maskininlärningsmodeller. Dessa problem skapar en betydande efterfrågan av hållbar maskininlärning. Hållbar maskininlärning har kapaciteten att träna modeller på en mindre datamängd, vilket minskar minne- och energiförbrukning under träningsprocessen. För att utforska hållbar maskininlärning analyserar denna avhandling Quantization-Aware Training, Model Distillation, Quantized Distillation, Continual Learning och en djupare evaluering av Siamesiska Neurala Nätverk (SNN), en av de mest lovande teknikerna inom hållbar maskininlärning. Empiriska utvärderingar utfördes med hjälp av flera olika datamängder för att illustrera potentialen hos dessa tekniker. Resultaten visar att energibesparingsteknikerna kan utnyttjas för att göra maskininlärningsmodeller mer hållbara utan att kompromissa för precision. Dessutom visar undersökningen av SNNs att de kan överträffa vanliga neurala nätverk, med och utan Continual Learning, även om de tränas på betydligt mindre data.

Dans cette thèse, nous prouvons des résultats de théorie spectrale, directe et inverse, dans la limite semi-classique, pour les opérateurs de Toeplitz autoadjoints sur les surfaces. Pour les opérateurs pseudo-différentiels, les résultats en question sont déjà connus, et il est naturel de vouloir les étendre aux opérateurs de Toeplitz. Les conditions de Bohr-Sommerfeld usuelles, qui caractérisent les valeurs propres proches d'une valeur régulière du symbole principal, ont été obtenues il y a quelques années seulement pour les opérateurs de Toeplitz. Notre contribution consiste en l'extension de ces conditions près de valeurs critiques non dégénérées. Nous traitons le cas d'une valeur critique elliptique à l'aide d'une technique de forme normale ; l'opérateur modèle est la réalisation de l'oscillateur harmonique sur l'espace de Bargmann, dont le spectre est bien connu. Dans le cas d'une valeur critique hyperbolique, la forme normale ne suffit plus et nous complétons l'étude en faisant appel à des arguments dus à Colin de Verdière et Parisse, à qui l'on doit le résultat analogue dans le cas pseudo-différentiel. Enfin, nous établissons un résultat de théorie spectrale inverse pour les opérateurs de Toeplitz autoadjoints sur les surfaces ; plus précisément, nous montrons que sous certaines hypothèses génériques, la connaissance du spectre à l'ordre deux dans la limite semi-classique permet de retrouver le symbole principal à symplectomorphisme près. Ce résultat s'appuie en grande partie sur l'écriture des règles de Bohr-Sommerfeld. / In this thesis, we prove some direct and inverse spectral results, in the semiclassical limit, for self-adjoint Toeplitz operators on surfaces. For pseudodifferential operators, these results are already known, and it is natural to expect their extension to the Toeplitz setting. The usual Bohr-Sommerfeld conditions, characterizing the eigenvalues close to a regular value of the principal symbol, have been obtained a few years ago for Toeplitz operators. Our contribution consists in extending these conditions near nondegenerate critical values. We handle the case of an elliptic value thanks to a normal form technique; the model operator is the realization of the harmonic oscillator in the Bargmann space, whose spectrum is well-known. In the case of a hyperbolic value, the normal form is no longer sufficient and we conclude by using additional arguments due to Colin de Verdière and Parisse, who derived the analogous result for pseudodifferential operators. Finally, we write an inverse spectral result for self-adjoint Toeplitz operators on surfaces; more precisely, we show that under some generic hypotheses, the knowledge of the spectrum up to order two in the semiclassical limit allows to recover the principal symbol up to symplectomorphism. This result essentially relies on Bohr-Sommerfeld rules.

La quantification par déformation et la correspondance de McKay forment les grands thèmes de l'étude qui porte sur des variétés algébriques singulières, des quotients d'algèbres de polynômes et des algèbres de polynômes invariants sous l'action d'un groupe fini. Nos principaux outils sont les cohomologies de Poisson et de Hochschild et la théorie des représentations. Certains calculs formels sont effectués avec Maple et GAP. Nous calculons les espaces d'homologie et de cohomologie de Hochschild des surfaces de Klein, en développant une généralisation du Théorème de HKR au cas de variétés non lisses et utilisons la division multivariée et les bases de Gröbner. La clôture de l'orbite nilpotente minimale d'une algèbre de Lie simple est une variété algébrique singulière sur laquelle nous construisons des star-produits invariants, grâce à la décomposition BGS de l'homologie et de la cohomologie de Hochschild, et à des résultats sur les invariants des groupes classiques. Nous explicitons les générateurs de l'idéal de Joseph associé à cette orbite et calculons les caractères infinitésimaux. Pour les algèbres de Lie simples B, C, D, nous établissons des résultats généraux sur l'espace d'homologie de Poisson en degré 0 de l'algèbre des invariants, qui vont dans le sens de la conjecture d'Alev et traitons les rangs 2 et 3. Nous calculons des séries de Poincaré à 2 variables pour des sous-groupes finis du groupe spécial linéaire en dimension 3, montrons que ce sont des fractions rationnelles, et associons aux sous-groupes une matrice de Cartan généralisée pour obtenir une correspondance de McKay algébrique en dimension 3. Toute l'étude a donné lieu à 4 articles / Deformation quantization and McKay correspondence form the main themes of the study which deals with singular algebraic varieties, quotients of polynomial algebras, and polynomial algebras invariant under the action of a finite group. Our main tools are Poisson and Hochschild cohomologies and representation theory. Certain calculations are made with Maple and GAP. We calculate Hochschild homology and cohomology spaces of Klein surfaces by developing a generalization of HKR theorem in the case of non-smooth varieties and use the multivariate division and the Groebner bases. The closure of the minimal nilpotent orbit of a simple Lie algebra is a singular algebraic variety : on this one we construct invariant star-products, with the help of the BGS decomposition of Hochschild homology and cohomology, and of results on the invariants of the classical groups. We give the generators of the Joseph ideal associated to this orbit and calculate the infinitesimal characters. For simple Lie algebras of type B, C, D, we establish general results on the Poisson homology space in degree 0 of the invariant algebra, which support Alev's conjecture, then we are interested in the ranks 2 and 3. We compute Poincaré series of 2 variables for the finite subgroups of the special linear group in dimension 3, show that they are rational fractions, and associate to the subgroups a generalized Cartan matrix in order to obtain a McKay correspondence in dimension 3. All the study comes from 4 papers

L’utilisation des modèles 3D, représentés sous forme de maillage, est sans cesse croissante dans de nombreuses applications. Pour une transmission efficace et pour une adaptation à l’hétérogénéité des ressources de ces modèles, des techniques de compression progressive sont généralement utilisées. Afin de protéger le droit d’auteur de ces modèles pendant la transmission, des techniques de tatouage sont également employées. Dans ces travaux de thèse, nous proposons premièrement deux méthodes de compression progressive pour des maillages avec ou sans information de couleurs et nous présentons finalement un système conjoint de compression progressive et de tatouage. Dans une première partie, nous proposons une méthode d’optimisation du compromis débit-distorsion pour des maillages sans attribut de couleur. Pendant le processus de l’encodage, nous adoptons la précision de quantification au nombre d’éléments et à la complexité géométrique pour chaque niveau de détail. Cette adaptation peut s’effectuer de manière optimale en mesurant la distance par rapport au maillage original, ou de façon quasi-optimale en utilisant un modèle théorique pour une optimisation rapide. Les résultats montrent que notre méthode donne des résultats compétitifs par rapport aux méthodes de l’état de l’art. Dans une deuxième partie, nous nous focalisons sur l’optimisation du compromis débit-distorsion pour des maillages possédant l’information de couleur attachée aux sommets. Après avoir proposé deux méthodes de compression pour ce type de maillage, nous présentons une méthode d’optimisation du débit-distorsion qui repose sur l’adaptation de la précision de quantification de la géométrie et de la couleur pour chaque maillage intermédiaire. Cette adaptation peut être effectuée rapidement selon un modèle théorique qui permet d’évaluer le nombre de bits de quantification nécessaire pour chaque maillage intermédiaire. Une métrique est également proposée pour préserver les éléments caractéristiques durant la phase de simplification. Finalement, nous proposons un schéma conjoint de compression progressive et de tatouage. Afin de protéger tous les niveaux de détails, nous insérons le tatouage dans chaque étape du processus d’encodage. Pour cela, à chaque itération de la simplification, nous séparons les sommets du maillage en deux ensembles et nous calculons un histogramme de distribution de normes pour chacun d’entre eux. Ensuite, nous divisons ces histogrammes en plusieurs classes et nous modifions ces histogrammes en décalant les classes pour insérer un bit. Cette technique de tatouage est réversible et permet de restaurer de manière exacte le maillage original en éliminant la déformation induite par l’insertion du tatouage. Nous proposons également une nouvelle méthode de prédiction de la géométrie afin de réduire le surcoût provoqué par l’insertion du tatouage. Les résultats expérimentaux montrent que notre méthode est robuste à diverses attaques géométriques tout en maintenant un bon taux de compression / The use of 3D models, represented as a mesh, is growing in many applications. For efficient transmission and adaptation of these models to the heterogeneity of client devices, progressive compression techniques are generally used. To protect the copyright during the transmission, watermarking techniques are also used. In this thesis, we first propose two progressive compression methods for meshes with or without color information, and we present a joint system of compression and watermarking. In the first part, we propose a method for optimizing the rate-distortion trade-off for meshes without color attribute. During the encoding process, we adopt the quantization precision to the number of elements and geometric complexity. This adaptation can be performed optimally by measuring the distance regarding the original mesh, or can be carried out using a theoretical model for fast optimization. The results show that our method yields competitive results with the state-of-the-art methods. In the second part, we focus on optimizing the rate-distortion performance for meshes with color information attached to mesh vertices. We propose firstly two methods of compression for this type of mesh and then we present a method for optimizing the rate-distortion trade-off based on the adaptation of the quantification precision of both geometry and color for each intermediate mesh. This adaptation can be performed rapidly by a theoretical model that evaluates the required number of quantization bits for each intermediate mesh. A metric is also proposed in order to preserve the feature elements throughout simplification. Finally, we propose a joint scheme of progressive compression and watermarking. To protect all levels of detail, we insert the watermark within each step of the encoding process. More precisely, at each iteration of simplification, we separate vertices into two sets and compute a histogram of distribution of vertex norms for each set. Then, we divide these histograms into several bins and we modify these histograms by shifting bins to insert a bit. This watermarking technique is reversible and can restore exactly the original mesh by eliminating the distortion caused by the insertion of the watermark. We also propose a new prediction method for geometry encoding to reduce the overhead caused by the insertion of the watermark. Experimental results show that our method is robust to various geometric attacks while maintaining a good compression ratio

[pt] Esta dissertação apresenta uma estratégia para desenvolver mecanismos de compressão de dados adquiridos por sensores, seguindo como inspiração o processo utilizado no formato JPG2000. A estratégia adota a abordagem das séries históricas dos dados sob o ponto de vista do processamento de sinais. Dada à natureza instável dos sensores é natural que ruídos sejam adicionados ao sinal original. Estes ruídos são detectados e tratados enquanto o sinal é suavizado e limpo, facilitando a análise, ao passo que em que componentes pouco relevantes são removidos ou aproximados, permitindo que o sinal seja comprimido com pouca perda de informação. / [en] This dissertation introduces a strategy to develop a compression method for sensor data inspired on the JPG2000 techniques. The strategy adopted processes data streams much in the same way as signal processing. Due to the unstable nature of sensor data, noise is added to the original signal. This noise is detected and treated while the signal is cleaned and smoothed, making it easier to analyze the data stream. Less relevant signal components are removed or approximated allowing the signal to be compressed with few information loss.

When calculating scattering amplitudes in gauge and gravitational theories one encounters infrared (IR) divergences associated with massless fields. These are known to be artifacts of constructing a quantum field theory starting with free fields, and the assumption that in the asymptotic limit (i.e. well before and after a scattering event) the incoming and outgoing states are non-interacting. In 1937, Bloch and Nordsieck provided a technical procedure eliminating the IR divergences in the cross-sections. However, this did not address the source of the problem: A detailed analysis reveals that, in quantum electrodynamics (QED) and in perturbative quantum gravity (PQG), the interactions cannot be ignored even in the asymptotic limit. This is due to the infinite range of the massless force-carrying bosons. By taking these asymptotic interactions into account, one can find a picture changing operator that transforms the free Fock states into asymptotically interacting Faddeev- Kulish (FK) states. These FK states are charged (massive) particles surrounded by a “cloud” of soft photons (gravitons) and will render all scattering processes infrared finite already at an S-matrix level. Recently it has been found that the FK states are closely related to asymptotic symmetries. In the case of QED the FK states are eigenstates of the large gauge transformations – U(1) transformations with a non-vanishing transformation parameter at infinity. For PQG the FK states are eigenstates of the Bondi-Metzner-Sachs (BMS) transformations – the asymptotic symmetry group of an asymptotically flat spacetime. It also appears that the FK states are related the Wilson lines in the Mandelstam quantization scheme. This would allow one to obtain the physical FK states through geometrical or symmetry arguments. We attempt to clarify this relation and present a derivation of the FK states in PQG from the gravitational Wilson line in the eikonal approximation, a result that is novel to this thesis.

Made available in DSpace on 2016-04-28T14:16:34Z (GMT). No. of bitstreams: 1 Douglas Guilherme Schmidt.pdf: 995968 bytes, checksum: 1a8192151fc433a54ec422f421249ac4 (MD5) Previous issue date: 2008-09-15 / Secretaria da Educação do Estado de São Paulo / This historical research analyses the initial period of construction of wave mechanics, as propounded by the Austrian physicist Erwin Schrödinger (1887- 1961), emphasizing his work from December 1925 to February 1926. During these months Schrödinger created the basis of his quantum theory and wrote his two earlier papers on this subject. They were published in the Annalen der Physik. The present dissertation analyses those two papers, and some of their precedents and immediate consequences. Special attention is given to the influence of the theory of matter waves of the French physicist Louis de Broglie (1892-1987) upon the development of Schrödinger s theory, as well as other works and relevant circumstances that contributed to the creation of wave mechanics. The dissertation also discusses the interpretation given by Schrödinger to his own theory, comparing it to the approach of other physicists of that time / O presente trabalho histórico investiga a fase inicial da construção da mecânica ondulatória formulada pelo físico austríaco Erwin Schrödinger (1887- 1961), dando especial atenção aos trabalhos por ele realizados de dezembro de 1925 até fevereiro de 1926. Nesse período, Schrödinger concebeu as bases de sua teoria quântica e redigiu os dois primeiros artigos sobre o assunto, publicados na revista Annalen der Physik. Esta dissertação analisa esses dois artigos, bem como alguns de seus precedentes e repercussões. É analisada em especial a influência da teoria de ondas de matéria do físico francês Louis de Broglie (1892- 1987) no desenvolvimento da teoria de Schrödinger, bem como outros trabalhos e circunstâncias importantes que contribuíram para a elaboração da mecânica ondulatória. Discute-se também a interpretação que o próprio Schrödinger deu à sua teoria, comparando-a com o enfoque adotado por outros físicos da época