Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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This thesis presents an improved method to calculate renormalization constants in a regularization invariant momentum scheme using twisted boundary conditions. This enables us to simulate with momenta of arbitrary magnitude and a fixed direction. With this new technique, together with non-exceptional kinematics and volume sources, we are able to take a statistically and theoretically precise continuum limit. Thereafter, all the running of the operators with momentum scale is due to their anomalous dimension. We use this to develop a practical scheme for step scaling with off shell vertex functions. We develop the method on 16³ × 32 lattices to show the practicality of using small volume simulations to step scale to high momenta. We also use larger 24³×64 and 32³×64 lattices to compute renormalization constants very accurately. Combining these with previous analyses we are able to extract a precise value for the light and strange quark masses and the neutral kaon mixing parameter BK. We also analyse eigenvectors of the domain wall Dirac matrix. We develop a practical and cost effective way to compute eigenvectors using the implicitly restarted Lanczos method with Chebyshev acceleration. We show that calculating eigenvectors to accelerate propagator inversions is cost effective when as few as one or two propagators are required. We investigate the technique of low mode averaging (LMA) with eigenvectors of the domain wall matrix for the first time. We find that for low energy correlators, pions for example, LMA is very effective at reducing the statistical noise. We also calculated the η and η′ meson masses, which required evaluating disconnected correlation functions and combining stochastic sources with LMA.

Bibliography : p. 105-111 / xi, 111 p. : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 184-188).

Made available in DSpace on 2016-05-17T16:51:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-08-29. Added 1 bitstream(s) on 2016-05-17T16:54:20Z : No. of bitstreams: 1 000854764.pdf: 562890 bytes, checksum: 164c6db1a3c04e45b5f0eea9ea15e58e (MD5) / Este trabalho é basicamente uma revisão de alguns aspectos de integrabilidade em duas dimensões discutidos no artigo Renormalization group flows and continual Lie algebras do professor Ioannis Bakas. A idéia é estudar o fluxo do grupo de renormalização das métricas bi-dimensionais nos modelos-'alfa' usando a função beta a 1-loop, e mostrar que elas fornecem análogos contínuos das equações de campo de Toda nas coordenadas conformemente planas do espaço target. Nesta formulção algébrica, a escala logaritmica de comprimento da folha mundo é interpretada como o parâmetro de Dynkin num sistema de raízes de uma álgebra de Lie contínua, denotada por G(d/dt;II), com um kernel de Cartan generalizado anti-simétrico K(t,t') = 'alfa'(t−t'). Usando o formalismo de curvatura zero construiremos a solução geral do fluxo do grupo de renormalização em termos das configurações de campo livre por meio de transformações de Bäcklund. A validade desta solução geral como uma expansão em serie de potência será testada com alguns exemplos especiais que incluim o modelo sausage, as métricas de curvatura constante negativa e a queda de singularidades côonicas / This work is basically a review of some aspect of the integrability in two dimensions discussed in the Prof. Ioannis Bakas's paper called Renormalization group flows and continual Lie algebras. The main idea is to study the renormalization group flow of two-dimensional metrics in sigma models using the one-loop beta function, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates in the target space. In this algebraic frame, the logarithm of the world-sheet length scale t is interpreted as Dynkin parameter on the root system of a continual Lie algebra, denoted by G(d/dt;II),witha an ti-symmetric generalized Cartan kernel K(t,t') ='sigmma'(t−t'). Using the zero curvature formalism, we construct a general solution of the renormalization group flow in terms of the free field configurations via B¨acklund transformations. The validity of these general solutions as a power series expansion is verified in some specials examples including the sausage model, the constant negative curvature metrics and the decay of conical singularities

Orientador: Abraham Hirsz Zimerman / Banca: Nathan Jacob Berkovits / Banca: Victor de Oliveira Rivelles / Resumo: Este trabalho é basicamente uma revisão de alguns aspectos de integrabilidade em duas dimensões discutidos no artigo "Renormalization group flows and continual Lie algebras" do professor Ioannis Bakas. A idéia é estudar o fluxo do grupo de renormalização das métricas bi-dimensionais nos modelos-'alfa' usando a função beta a 1-loop, e mostrar que elas fornecem análogos contínuos das equações de campo de Toda nas coordenadas conformemente planas do espaço target. Nesta formulção algébrica, a escala logaritmica de comprimento da folha mundo é interpretada como o parâmetro de Dynkin num sistema de raízes de uma álgebra de Lie contínua, denotada por G(d/dt;II), com um kernel de Cartan generalizado anti-simétrico K(t,t') = 'alfa'(t−t'). Usando o formalismo de curvatura zero construiremos a solução geral do fluxo do grupo de renormalização em termos das configurações de campo livre por meio de transformações de Bäcklund. A validade desta solução geral como uma expansão em serie de potência será testada com alguns exemplos especiais que incluim o modelo "sausage", as métricas de curvatura constante negativa e a queda de singularidades côonicas / Abstract: This work is basically a review of some aspect of the integrability in two dimensions discussed in the Prof. Ioannis Bakas's paper called "Renormalization group flows and continual Lie algebras". The main idea is to study the renormalization group flow of two-dimensional metrics in sigma models using the one-loop beta function, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates in the target space. In this algebraic frame, the logarithm of the world-sheet length scale t is interpreted as Dynkin parameter on the root system of a continual Lie algebra, denoted by G(d/dt;II),witha an ti-symmetric generalized Cartan kernel K(t,t') ='sigmma'(t−t'). Using the zero curvature formalism, we construct a general solution of the renormalization group flow in terms of the free field configurations via B¨acklund transformations. The validity of these general solutions as a power series expansion is verified in some specials examples including the sausage model, the constant negative curvature metrics and the decay of conical singularities / Mestre