Quantum gauge theories

• Grant number: 19/02316-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2019
• End date: November 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Enrico Bertuzzo
• Grantee: Milena Bastos Albino
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This introduction to research project aims at the explicit construction of quantum electrodynamics (QED). To this end, we will first study the many-body non-relativistic quantum mechanics formalism, observing how it is equivalent to a field theory quantized according to canonical quantization. We will then study the formulation of relativistic quantum mechanics, coming to the conclusion that this theory only makes sense as a quantum field theory. In addition, we will study how fields can be classified in terms of representations of the Lorentz group and written in terms of the operators that create and destroy particles. Finally, we will study in detail the quantum origin of gauge invariance and properly formulate quantum electrodynamics.