A presente dissertação revisa um modelo, de autoria de C. Dappiaggi, K. Fredenhagen e N. Pinamonti, de um campo escalar real quântico não-interagente acoplado com a métrica de um espaço-tempo FLRW (Friedmann-Lemaítre-Robertson-Walker). Apresentamos a metodologia de quantização de campos de Klein-Gordon reais em espaçostempos globalmente hiperbólicos e discorremos sobre o procedimento de regularização do tensor de energia-momento via point-splitting. Consideramos os campos em espaços FLRW e estados adiabáticos com flutuação média de campo dado por h2i = m2 +R, com ; constantes provenientes do procedimento de regularização. A retroação do campo quântico gera a equação diferencial para o parâmetro de Hubble H(t) dada por _H (H2H2 c ) = (H2H2+ )(H2H2 ) com Hc uma constante e H pontos críticos estáveis da equação. Esse simples modelo mostra que efeitos quânticos podem, por si só, fornecer fases de de Sitter estáveis sem adição de uma constante cosmológica a priori. Mesmo que de caráter apenas qualitativo, tal resultado indica que análises cautelosas de processos de quantização são importantes para análise de efeitos cosmológicos de teorias quânticas de campos em espaços curvos. / The present dissertation reviews the coupling of a scalar non-interacting quantum field with the metric of a FLRW(Friedmann-Lemaítre-Robertson-Walker) spacetime, proposed in a work by C. Dappiaggi, K. Fredenhagen and N. Pinamonti. We present methods for the quantization of a real Klein-Gordon field in globally hyperbolic spacetimes and discuss procedures for the point-splitting regularization of the stress-energy tensor. We consider those fields in FLRWspacetimes and point out adiabatic states with mean field fluctuation given by h2i = m2+R, with ; being constants that emerge from the regularization procedure. The backreaction of the quantum field provides a diferential equation for the Hubble parameter given by _H (H2H2 c ) = (H2H2+)(H2H2) with Hc a constant and H stable critical points of the equation. In this way, this simple model demonstrates that quantum efects may, by themselves, exibit stable de Sitter phases even without an introduction of a cosmological constant by hand. Althoug in a qualitative way, such result shows that, when dealing with the backreaction issue, a careful analysis of the quantization procedures is important for the analysis of cosmological efects of models of quantum field theories in curved spacetimes.

Neste trabalho, discutimos alguns aspectos das teorias quânticas de campos não comutativas; renormalização, mistura infravermelha-ultravioleta, e consistência perturbativa. Tais aspectos são tratados através da análise das versões não-comutativas dos modelos de teorias quânticas de campos; em especial estudamos o modelo \'CP POT.N-1\' não-comutativo e suas respectivas extensões; minimal e supersimétrica. / In this work, we shall discuss some aspects of noncommutative quantum field theories; renormalization, ultraviolet-infrared mixing and perturbative consistency. Such topics have been developed through the analysis of noncommutative versions of quantum field theory models, in particular, we study the CP N-1 model and its extensions; minimal and supersymmetric.

Nesta tese estudamos possíveis extensões do modelo CPN-1 em (2+1) dimensões. Provamos que quando tomado na representação fundamental à esquerda ele é renormalizável e não possui divergências infravermelhas perigosas. O mesmo não ocorre se o campo principal . Mostramos que a inclusão de férmions, minimamente acoplados ao campo de calibre, traz alguma melhoria no comportamento das divergências infravermelhas no setor de calibre em ordem dominante em 1/N. Discutimos também a invariância de calibre no procedimento de renormalização. / In this thesis investigate possible extensions of the (2+1) dimensional CPN-1 model to the noncommutative space. Up to leading nontrivial order of 1/N, we prove that the model restricted to the left fundamental representation is renormalizable and does not have dangerous infrared divergences. By contrast, IF the pricipal Field transforms in accord with the adjoint representation, linearly divergent, nonintegrable singularities are present in the two point function of the auxiliary gauge Field and also in the leading correction to the self-energy of the Field. It is showed that the inclusion of fermionic matter, minimally coupled to the gauge Field, ameliorates this behavior by eliminating infrared divergences in the gauge sector at the leading 1/N order. Gauge invariance of the renormalization is also discussed.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22245号 / 理博第4559号 / 新制||理||1655(附属図書館) / 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 田中 貴浩, 教授 川合 光, 教授 向山 信治 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis is devoted to the investigation of the phenomenon of quantum radiation -- i.e. the conversion of the (virtual) quantum fluctuations of a quantised field into (real) particles owing to the influence of external conditions. For that purpose a canonical particle (and thereby vacuum) definition is presented for a quantum field in the presence of specific external conditions. Utilising this set-up the number of Rindler particles in the Minkowski vacuum is calculated explicitly where the Unruh effect is recovered. Focusing on the gravitational collapse of an object the number of created particles accounting for the Hawking effect is derived and the dependence of the results on the dynamics of the collapse is discussed. Furthermore the influence of finite initial temperatures is investigated for a weakly time-dependent perfectly conducting cavity (dynamical Casimir effect), a dynamical dielectric medium, and the Friedmann-Robertson-Walker metric. Finally the problems arising from the consideration of interacting fields are outlined by means of a simple example.

De nombreuses approches à la gravité quantique suggèrent que la description usuelle de l’espace-temps ne serait pas adaptée à la description des phénomènes physiques impliquant à la fois des processus gravitationnels et quantiques. Une meilleure description pourrait consister à munir l’espace-temps d’une structure non-commutative en remplaçant les coordonnées locales sur la variété par des opérateurs ne commutant pas deux-à-deux. Il s’ensuit que le comportement des théories de champs construites sur de tels espaces diffère en général de celui des théories de champs ordinaires. L’étude de ces possibles nouvelles propriétés est l’objet de la théorie non-commutative des champs (TNCC) dont nous étudions certains des aspects.Dans le présent mémoire, nous considérons deux familles d’espaces quantiques dont l’algèbres de coordonnées admet une structure d’algèbre de Lie. La première famille est caractérisée par l’algèbre su(2) et apparait dans le cadre de modèle de gravité quantique en 3 dimensions, ainsi que dans certains modèles de « brane » et de « group field theory ». La seconde famille d’espaces quantiques est connue sous le nom de kappa-Minkowski. L’intérêt de cet espace réside dans le fait qu’il est défini comme l’espace homogène associé à l’algèbre de Hopf de kappa-Poincaré. Cette dernière définit une déformation, à l’échelle de Planck, de l’algèbre de Poincaré et s’avère être étroitement liée à certains modèles de gravité quantique.Afin d’étudier les TNCC, il est commode de représenter l’espace quantique comme une algèbre non-commutative de fonctions munie d’un produit déformé appelé « star-product ». Une façon canonique de construire un tel produit consiste à se servir d’outils d’analyse harmonique et à adapter le schéma de quantification de Weyl (originellement introduit dans le cadre de la mécanique quantique) à l’algèbre considérée. Les expressions de star-product associé aux espaces susmentionnés sont dérivées de manière explicite. Nous montrons en particulier que des familles de star-product inéquivalents peuvent être classifiées par des considérations cohomologiques. Nous étudions enfin les propriétés quantiques de différents modèles de TNCC scalaire quartique construits à l’aide de ces star-product. Dans le cas où l’espace quantique est caractérisé par l’algèbre su(2), nous trouvons que la fonction 2-point est fini à l’ordre une boucle, le paramètre de déformation jouant le rôle d’une coupure ultraviolette et infrarouge. Dans le cas de kappa-Minkowski, nous insistons sur l’invariance sous kappa-Poincaré de l’action fonctionnelle et montrons que certains modèles de TNCC scalaire quartique divergent moins que dans le cas commutatif. Par ailleurs, la fonction 4-point est trouvée finie à l’ordre une boucle. Nos résultats, ainsi que leurs conséquences, sont finalement discutés. / As many theoretical studies point out, the classical description of spacetime, as a continuum, might be no longer adequate to reconcile gravity with quantum mechanics at very high energy (the relevant energy scale being often regarded as the Planck scale). Instead, a more appropriate description could be provided by the data of a noncommutative algebra of coordinate operators replacing the usual commutative local coordinates on smooth manifold. Once the noncommutative nature of spacetime is assumed, it is to expect that the (classical and quantum) properties of field theories on noncommutative background differ from the ones of field theories on classical background. This is the aim of Non-Commutative Field Theory (NCFT) to explore and study these new properties.In the present dissertation, we consider two families of quantum spacetimes of Lie algebra type noncommutativity. The first family is characterised by su(2) noncommutativity and appears in the description of some models of quantum gravity in 3-dimensions. The other family of quantum spacetimes is known in the physics literature as the 4-d kappa-Minkowski space. The importance of this quantum spacetime lies into the fact that its symmetries are provided by the (quantum) kappa-Poincaré algebra (a deformation of the classical Poincaré algebra) together with the fact that the deformation parameter 'kappa', which is of mass dimension, provides a natural energy scale at which the quantum gravity effects may be relevant (and is often regarded as being related to the Planck scale). For these reasons, the kappa-Minkowski space appears as a good candidate for a spacetime to be involved in the description of Doubly Special Relativity and Relative Locality models.To study NCFT it is often convenient to introduce a star product characterising the (noncommutative) C*-algebra of fields modelling the quantum spacetime under consideration. We emphasise that a canonical star product can be obtained by using the group algebraic structures underlying the construction of such Lie algebra type quantum spaces, namely by making use of harmonic analysis on the corresponding Lie group together with the Weyl quantisation scheme. The explicit derivation of such star product for kappa-Minkowski is given. In addition, we show that su(2) Lie algebras of coordinate operators related to quantum spaces with su(2) noncommutativity can be conveniently represented by SO(3)-equivariant poly-differential involutive representations and show that the quantized plane waves obtained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for SU(2). We finally indicate a convenient way to extend this construction to other semi-simple but non simply connected Lie groups by making use of results from group cohomology with value in an abelian group that would replace the constraints stemming from the simple Wigner theorem.Then, we investigate the quantum properties of various models of interacting scalar field theory on noncommutative background making use of the aforementioned star product formalism to construct physically reasonable expressions for the action functional. Considering quantum spacetime with su(2) noncommutativity, we find that the one-loop 2-point function for complex scalar field theories with quartic interactions is finite, the deformation parameter playing the role of a natural UV cut-off. Special attention is paid to the derivation of the one-loop corrections to both the 2-point and 4-point functions for various models of kappa-Poincaré invariant scalar field theory with quartic interactions. In that case, we show that for some models the 2-point function divergences linearly thus slightly milder than their commutative counterpart, while the one-loop 4-point function is shown to be finite. The results we obtained together with their consequences are finally discussed.

In this work, we study two problems in quantum field theory from a boundary point of view. Our perspective is motivated by the bootstrap philosophy, which aims to understand how principles such as kinematics, unitarity, and symmetry constrain physical observables. Regarding kinematics, we actually first relax the unitarity constraint and investigate thenon-unitary representations of the boundary superconformal algebra for AdS4 with N = 2 supercharges. In particular, we identify multiplets containing partially massless (PM) fields, as well as other exotic shortening conditions and structures exclusive to the nonunitary regime. Then, turning on interactions, we study a problem centered in dynamics: we investigate the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. In particular, we highlight the so-called exceptional scalar field theories, which are the nonlinear sigma model, Dirac-Born-Infeld, and (special) galileon theories. We find that nonlinearly realized symmetries imply soft theorems which must be obeyed by the wavefunction. Moreover, we develop bootstrap techniques utilizing this information along with the singularity structure of the wavefunction to fix its form. In addition, we systematize this construction into a novel set of recursion relations.

In this thesis, we extend the numerical S-matrix bootstrap program to 1+1d theories with a boundary, where we bootstrap the 1-to-1 reflection matrix (R-matrix). We review the constraints that a physical R-matrix must obey, namely unitarity, analyticiy and crossing symmetry. We then carve out the allowed space of 2d R-matrices with the O(N) nonlinear sigma model and the periodic Yang Baxter solution in the bulk. We find a variety of integrable R-matrices along the boundary of the allowed space both with and without free parameters. The integrable models without a free parameter appear at vertices of the allowed space, while those with a free parameter occupy the whole boundary. We also introduce the extended analyticity constraint where we increase the domain of analyticity beyond the physical region. In some cases, the allowed space of R-matrices shrinks drastically and we observe new vertices which correspond to integrable theories. We also find a new integrable R-matrix through our numerics, which we later obtained by solving the boundary Yang--Baxter equation. Finally, we derive the dual to the extended analyticity problem and find that the formalism allows for R-matrices which do not saturate unitarity to lie on the boundary of the allowed region.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19896号 / 工博第4212号 / 新制||工||1651(附属図書館) / 32973 / 京都大学大学院工学研究科マイクロエンジニアリング専攻 / (主査)教授 立花 明知, 教授 木村 健二, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This report aims to give an insight to the path integral formalism in quantum mechanics. After explaining the kernel's construction, some of its properties and ways to compute it, we see how it relates to the Schrödinger picture. Moreover, we see how its representation can change if it is defined in the space, momentum, time or energy space. Finally, we derive Born's expansion with the kernel showing how this formalism helps to understand perturbation theory and thus scattering. The path integral formalism is then used in quantum field theory with proofs and examples of simple correlation functions. Furthermore, supersymmetry in zero and one dimension are studied with use of the localization principle and the Witten index.