Uma Revisão de Modelos Bidimensionais em Teoria Quântica dos Campos

• Ano de defesa: 2007
• Autor(a) principal: Rodrigues, Armando Flavio
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Programa de Pós-graduação em Física; Física
• Palavras-chave em Português: Eletrodinâmica Quântica; Teoria de Campo; Cromodinâmica Quântica.; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://app.uff.br/riuff/handle/1/18693

Since the seminal work by Walter Thirring, in 1958, when he created the first exactly solvable, non-perturbative bidimensional model in Quantum Field Theory, amazing and explicative results have been obtained in the copious literature that followed. Notwhitstanding that, the complexity of the matter (no double sense here) has also produced some obscurity and confusion of ideas in respect of the correct applicability of some methods of analysis, leading sometimes to different and unsatisfactory results. I m just presenting here, with the main aim of to cast a tenuous light on these researches gray zones, and concerned to found the methodology upon the most basic clearness, a work that intents to fill some delicate gaps in that literature. To begin with, the Thirring-Wess model is newly seen through a functional integral approach, and using the Abelian reduction of the Wess-Zumino-Witten (WZW) theory, the isomorphism between the QED2 (QCD2), with broken gauge symmetry by a regularization prescription, and the Abelian (non-Abelian) Thirring-Wess model with a fixed bare mass for the meson field, is established. The second part deals with another application of the WZW theory in two dimensions, the functional integral bosonization of the two-dimensional fermion model with interaction among N different massive field species is obtained. The operator solution for the quantum equations of motion is reconstructed from the functional integral formalism. Through an extension of the existent approaches, the partition function of the statistical mechanical system associated with the effective bosonized theory is obtained, and the exact equation of state exhibits a Kosterlitz-Thouless phase transition. Finally, at the third and fourth parts, the characteristics of the hidden quartic Thirring interaction underneath the derivative coupling model (and its avatars), in which a massive Fermi field interacts with massless Bose fields, are clarified and delimited within the operator formalism. This last topic has had a controversial career ab ovo, seeing that its results do not confirm those of some old and recent papers, e.g. the long-time supposed and widespread belief in the full equivalence between the Thirring and the Rothe-Stamatescu models considered in the m0 = 0 limit.