The problem of Gauge fixation in the action and the duality in D = 2 + 1 dimensions

• Grant number: 19/01372-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): April 01, 2019
• Effective date (End): December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Denis Dalmazi
• Grantee: Felipe Augusto da Silva Barbosa
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

A basic concept in Field Theory and Elementary Particle Physics is gauge symmetry. The most fundamental theories as the standard model (electro-weak-strong interactions), gravitational theories and even superstrings have local symmetries (gauge symmetries). Although the gauge principle leads us to an inspiring and aesthetically attractive formulation of the fundamental forces in Nature, in practice, for sake of simplicity, we are usually led to fix a gauge condition, which breaks gauge symmetry. However, this must be done in such way that the physical content of the model is no modified. Many gauge choices can be implemented but some of them lead to Gribov problem or to an incorrect counting of degrees o freedom. We must be especially careful when gauge conditions are implemented at action level before the derivation of the equations of motion. Though this procedure usually leads to simplified expressions, we may loose some equations of motion which can not be recovered from the remaining ones. This issue has been recently discussed in the literature, especially regarding scalar-tensor and bimetric models. In present work the student will be introduced to the gauge fixing subject by means of toy models with finite number of degrees of freedom altogether with examples in field theory as the usual Maxwell electrodynamics and the Maxwell Chern-Simons model in D=2+1. Our aim is to pave the way for a future master degree research plan in field theory.