Quantum field theory with indefinite metric, from planar models in condensed matter, spontaneous symmetry breaking mechanisms and Elko spinors, to dual reducible higher order theories

• Grant number: 21/12126-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2022
• End date: August 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Roldão da Rocha
• Grantee: Gabriel Brandão de Gracia
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The present project is related to the analysis and quantization of two different classesof field theories. In the first front we will study planar models in the context of condensed matter and models with mass generation mechanisms. In the second front, the theories with higher order derivatives and also dual models via tensor fields with a higher rank than the original theory will be analysed. Therefore, we intend to investigate the properties of these models when the matter sector is represented by the conventional Dirac fermions and also for the of mass dimension 1 fermions, the so called Elko spinor. The unity bond between these two different fronts is represented by the use of the covariant quantization formalism by means of the introduction of the auxiliary B field inthe Heisenberg description. This is the Kugo-Ojima-Nakanishi (KON) formalism. This method employs an indefinite Hilbert space metric and is particularly useful in gauge theories. The fundamental objects are the field commutators and the Källén-Lehmman (KL) representation for the radiative structure. It allows a powerful non-perturbative characterization of the studied model and has also a perturbative version. By means of this organizing principle we intend to build ghost and gauge fixing sectors that leadto a system without any quantum ambiguity. Therefore, we use auxiliary quantization methods according to each specific model analysed. We are going to use the perturbative version of the (KON) formalism and also a path integral approach in the BRST symmetry context for the first front of study in order to model the quantum Hall effect, described by the Chern-Simons model coupled to topological two band models, and also the electrodynamics in a non-linear gauge coupled to fermions and symmetry breaking matter. The arising results and methods can be used for the second front of analysed models inwhich we focus on an extension of the auxiliary field method for higher order theories as, for example, the Podolski one, and for the mentioned dual theories which generally present degree of freedom discontinuity at their mass less limit. Therefore, understanding the Hilbert space structure at this limit is a first good objective. In order to complete the proposal of this second front of the project, we analyse a way to obtain the complicate ghost of structure of their functional generator, that is typical of those dual models that often present reducible constraints, by means of the philosophy of the auxiliary field method, that is, eliminating any quantum ambiguity as a principle. We also intend to obtain the 1 loop renormalized structure for these models for the case of interaction with the Elko spinor. Another feasible objective is the analysis of a dual tensor theory for electromagnetism by means of the study of the Feynman graphs, that is, considering the model interacting with matter, and then deriving the new vertices, the Ward identities for the local symmetries and investigate if there is map connecting this model and its dual analogously to what is verified, by means of a master action, in the free case. We also add a mass term which, although break part of the reducible symmetry, preserves the U(1) symmetry and is unitary, having in mind the optical theorem, if one consider a given classof possible interactions. (AU)