Classical-quantum mechanical systems symmetric by the action of a Lie group

• Grant number: 17/11677-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2017
• End date: September 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Paulo de Magalhaes Rios
• Grantee: Arthur Couto Rosa Dutra de Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this project is to introduce the student to the research area of mathematical physics and symplectic geometry which focus on the study of the correspondence between classical and quantum mechanical conservative sistems that are symmetric by the action of a Lie group. To achieve this goal we will be guided by the book Symbol Correspondences for Spin Systems, that studies this problem in the context of conservative mechanical systems that are symmetric by the action of the group SU(2), the so called spin systems.In the first part of the project the student will study differential symplectic geometry, used to model classical Hamiltonian systems, and also basic elements of Lie groups and their representations. Starting in the second part we will closely follow chapters 3-8 of the main book to, in the end, tackle some open problems. (AU)