Working towards a gauge-invariant description of the Higgs model: from local composite operators to spectral density functions

• Ano de defesa: 2020
• Autor(a) principal: Egmond, Duive Maria Van
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade do Estado do Rio de Janeiro; Centro de Tecnologia e Ciências::Instituto de Física Armando Dias Tavares; Brasil; UERJ; Programa de Pós-Graduação em Física
• Palavras-chave em Português: Teoria quântica de campos; Teoria de Yang-Mills; Campos de calibre (Física); Bósons de Higgs; Simetria (Física); Quantum Field Theory; Gauge-Higgs systems; Mass generation; Sistemas de Gauge-Higgs; Geração de massa; CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DAS PARTICULAS ELEMENTARES E CAMPOS
• Link de acesso: http://www.bdtd.uerj.br/handle/1/21977

We analyze different BRST invariant solutions for the introduction of a mass termin Yang-Mills (YM) theories. First, we analyze the non-local composite gauge-invariantfield Ahµ(x), which can be localized by the Stueckelberg-like field ξa(x). This enables usto introduce a mass term in the SU(N) YM model, a feature that has been indicated ata non-perturbative level by both analytical and numerical studies. The configuration ofAh(x) , obtained through the minimization ofRd4xA2along the gauge orbit, gives riseto an all orders renormalizable action, a feature which will be illustrated by means of aclass of covariant gauge fixings which, as much as ’t Hooft’s Rξ-gauge of spontaneouslybroken gauge theories, provide a mass for the Stueckelberg-like field. Then, we considerthe unitary Abelian Higgs model and investigate its spectral functions at one-loop order.This analysis allows to disentangle what is physical and what is not at the level of theelementary particle propagators, in conjunction with the Nielsen identities. We highlightthe role of the tadpole graphs and the gauge choices to get sensible results. We alsointroduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massivephoton which, like the non-Abelian Curci-Ferarri model, is left invariant by a modifiednon-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly fromthe spectral function viewpoint. This provides a functional analogue of the Ojima ob-servation in the canonical formalism: there are ghost states with nonzero norm in theBRST-invariant states of the Curci-Ferrari model. Finally, the spectral properties of aset of local gauge-invariant composite operators are investigated in the U(1) and SU(2)Higgs model quantized in the ’t Hooft Rξgauge. These operators enable us to give agauge-invariant description of the spectrum of the theory, thereby surpassing certain in-commodities when using the standard elementary fields. The corresponding two-pointcorrelation functions are evaluated at one-loop order and their spectral functions are ob-tained explicitly. It is shown that the spectral functions of the elementary fields sufferfrom a strong unphysical dependence from the gauge parameter ξ, and can even exhibitpositivity violating behaviour. In contrast, the BRST invariant local operators exhibit awell defined positive spectral density.