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Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and real contributions to a given cross section are summed and smeared against an experimental resolution. In this thesis we treat the infrared problem formally in the language of distribution theory so that we can remove the divergences with local momentum space subtractions using Hadamard's procedure. This is analogous with the BPHZ mechanism for removing UV divergences. Our aim is to show how it is possible to make both the real and virtual subtractions analytically such that we are left with manifestly finite integrands. For the virtual graphs we present a new decomposition of the integrand in momentum space and remove those terms that are divergent. For the real graphs we show how the Taylor expansion of the momentum conserving delta function allows the explicit removal of the divergent part; furthermore we show that the homogeneous properties of the soft structure greatly simplifies this procedure.

One of the key goals of string theory is to provide a uni cation of general relativity and quantum eld theory. In the pursuit of this goal it has become clear that the di erent string theories that have been discovered so far are all in fact, partial descriptions of a single theory. At strong coupling a new theory, called M-theory, is the correct description. M-theory includes gravitons, M2-branes and M5-branes. Up to now, the correct description of the M5-brane is outstanding. In this project some proposals for this theory are studied. In particular, there is a proposal that D=5 maximally supersymmetric Yang-Mills theory can be used to provide a description of the world volume physics of the M5-brane. According to this proposal, instantons in D=5 maximally supersymmetric Yang-Mills theory are graviton excitations of the M theory. In this M.Sc dissertation the instanton solutions of D=5 maximally supersymmetric Yang-Mills theory are explored, with the goal of testing the above proposal. The dissertation begins with a review of the uses of instantons in quantum mechanics. In particular, instantons are used to account for tunneling e ects within a path integral approach to quantum mechanics. The lifting of ground state degeneracies as well as the estimation of the lifetime of unstable states using instantons is developed. The quantization of gauge theories is reviewed in detail. The relevance of instantons for a semi-classical study of Yang-Mills theory is explained. Finally, the relevance of instantons for D = 5 maximally supersymmetric Yang-Mills theory is considered.

Nesta tese, um estudo é feito do modelo bi-dimensional descrito pela densidade de Lagrangeana. Na primeira parte deste trabalho, discute- se a teoria de perturbação na constante de acoplamento g para as funções de Green. Mostra-se como e possível construir um esquema de renormalização de modo que não sejam induzidas interações quadri-lineares nos férmions quando M=0. Aplicando a identidade de Ward da corrente axial, prova-se então, que o limite M = 0 coincide, em qualquer ordem de g, com as funções de Green do modelo com massa do fermion nula, que e exatamente solúvel. Na segunda parte da tese , o termo de massa do férmion em L é tratado como uma perturbação em torno da teoria não livre. Após uma resomação parcial da série perturbativa, mostra-se que as funções de Green Euclidianas tornam-se finitas no intervalo O g POT. 2< pela introdução de um contra-termo proporcional a (:cos2g:1). A quebra da invariança pelas transformações - POT. 5 é verificada explicitamente por meio da identidade de Ward da corrente axial. / In this thesis, a study is made of the two-dimensional model described by the Lagrangean density. In the first part of this work, the perturbation theory in the coupling constant g is discussed for the Green functions. It is shown how to construct a renormalization scheme such that no four-linear interactions in the fermion field are induceded when m=0 by applying the axial current Ward identity, it is then proved that the M=O limit agrees, in every order of g, with the Green functions of the soluble model with massless fermion. In the second part of the thesis, the fermion mass term in L is considered as a perturbation on the interacting theory. After a partial resummation of the perturbative series, it is shown that the Euclidean Green functions are made finite for 0g²< introducing a counter-term proportional to (:cos2g:1). Breaking of -5 symmetry is explicity verified through the axial current Ward identity.

Ho Lai-yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 53-56). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Peierls Transition --- p.3 / Chapter 2.1 --- The Start of the Idea --- p.3 / Chapter 2.2 --- Peierls Transition in Second Quantization Representation --- p.5 / Chapter 2.3 --- Effect of Peierls Transition on an Antiferromagnetic Chain --- p.6 / Chapter 2.4 --- Evidence of Spin-Peierls Transition --- p.9 / Chapter 2.5 --- Materials with Spin-Peierls Transition --- p.11 / Chapter 3 --- Mean Field Calculations --- p.15 / Chapter 3.1 --- Jordan-Wigner Transformation --- p.15 / Chapter 3.2 --- Diagonalization of the XY Model --- p.17 / Chapter 3.3 --- Hartree-Fock Approximation --- p.19 / Chapter 3.4 --- Quantum Effect of Lattice --- p.21 / Chapter 4 --- Bosonization --- p.25 / Chapter 4.1 --- Continuum Limit --- p.25 / Chapter 4.2 --- Bosonization --- p.28 / Chapter 4.3 --- Relaxation of the Restriction on Lattice Distortion --- p.36 / Chapter 4.4 --- More Discussion on the Phase Hamiltonian --- p.39 / Chapter 4.5 --- Limitation of the Bosonization Technique and the Phase Hamil- tonian Approach --- p.41 / Chapter 5 --- Effect of Doping Impurities on Spin-Peierls Model --- p.43 / Chapter 5.1 --- Experimental Results --- p.43 / Chapter 5.2 --- Analytical Calculations of Doping Effect --- p.44 / Chapter 5.3 --- Criticism on the Calculations --- p.50 / Chapter 6 --- Summary and Conclusions --- p.52 / Bibliography --- p.53 / Chapter A --- Random-Phase Approximation --- p.57

Hoi-Yin Shik. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 92-94). / Text in English; abstracts in English and Chinese. / Hoi-Yin Shik. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Heisenberg Model --- p.1 / Chapter 1.2 --- Exactly Soluble Model --- p.3 / Chapter 1.3 --- This Project --- p.4 / Chapter 2 --- Spin-1 Net Spin Models --- p.6 / Chapter 2.1 --- Solution for the Four Spin Plaquette --- p.8 / Chapter 2.2 --- The Ground State and First Excited State Properties --- p.17 / Chapter 2.2.1 --- Spin Ladder Model --- p.18 / Chapter 2.2.2 --- Double Layer Model --- p.24 / Chapter 2.3 --- Excitation Spectrum for L Goes from One to Infinity --- p.27 / Chapter 2.4 --- General Spin S --- p.28 / Chapter 3 --- Constructing Exactly Soluble Quantum Spin Models --- p.29 / Chapter 3.1 --- Spin-1 Bond Operators --- p.29 / Chapter 3.1.1 --- Net Spin Ladder --- p.30 / Chapter 3.1.2 --- Spin Layer --- p.33 / Chapter 3.2 --- Other Two-dimensional Exactly Soluble Model --- p.35 / Chapter 3.3 --- Three-dimensional Model --- p.38 / Chapter 3.4 --- Spin-1 bond Operators --- p.56 / Chapter 3.5 --- Three-dimensional Spin-1 Model --- p.65 / Chapter 3.5.1 --- Other Exact Soluble Spin-1 Models --- p.68 / Chapter 3.6 --- General Spin-S --- p.68 / Chapter 4 --- Low Lying Excitations for the Net Spin Ladder --- p.72 / Chapter 4.1 --- Solutions of K-Rung Ladder --- p.74 / Chapter 4.1.1 --- K = 1 --- p.74 / Chapter 4.1.2 --- K = 2 --- p.75 / Chapter 4.1.3 --- K = 3 --- p.76 / Chapter 4.1.4 --- K = 4 --- p.78 / Chapter 4.1.5 --- K > 4 --- p.80 / Chapter 4.2 --- The Critical Point --- p.81 / Chapter 5 --- Conclusion --- p.90 / Bibliography --- p.92 / Chapter A --- The matrix represention of different Hamiltonians --- p.95 / Chapter A.1 --- p.95 / Chapter A.2 --- p.97 / Chapter A.3 --- p.99

Orientador: Donato Giorgio Torrieri / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T05:31:14Z (GMT). No. of bitstreams: 1 Truran_HenriqueDias_M.pdf: 940156 bytes, checksum: 80a833549f8b10145a3af3b38fc79eca (MD5) Previous issue date: 2017 / Resumo: Teoria quântica de campos é uma das mais bem sucedidas teorias da física contemporânea, e suas aplicações no estudo de sistemas acelerados um interessante tópico de pesquisa. De termalização em física de íons pesados à radiação de eletrons em QED de alta intensidade, o estudo de TQC em referenciais acelerados parece mais relevante do que nunca. Nessa dissertação nós apresentamos uma introdução aos princípios da teoria quântica de campos, como podemos estuda-la em referenciais acelerados, e como relacionar a física que um observador acelerado vê com os fenômenos observados no referencial inercial do laboratório / Abstract: Quantum field theory is one of the most successful theories of contemporary physics, and its applications to the study of accelerated systems an interesting topic of research. From thermalization in heavy-ion physics to radiation emission by electrons in high-intensity QED, the study of QFT in accelerated reference frames seems more relevant than ever. In this thesis we present an introduction to the principles quantum field theory, how we can study it in accelerated reference frames, and how to relate the physics seen by an accelerated observer's point of view with the phenomena observed in the inertial frame of the laboratory / Mestrado / Física / Mestre em Física / 132651/2015-7 / CNPQ

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The Kapitza-Dirac effect is similar to the canonical experiment on diffraction of electrons through slits in an opaque screen, except that the diffraction grating has been replaced by a standing wave of light. Remarkably, incident electrons are diffracted by the standing light wave almost as if by a standard diffraction grating. Only recently has this effect been confirmed experimentally in this form [1], although it was originally predicted by Kapitza and Dirac almost 70 years ago. This paper examines the relativistic effects involved in this phenomena using the formalism of quantum field theory.