Symmetries, Invariants and Conservation Laws

• Grant number: 24/01570-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2024
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Miled Hassan Youssef Moussa
• Grantee: Diogo Macedo de Mello
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims, firstly, to study Noether's theorem within the scope of classical mechanics, which involves the concepts of symmetries, invariants and conservation laws. Secondly, we intend to extend this study and the concepts itbrings to the scope of pseudo-Hermitian quantum mechanics. In this domain, we must address autonomous and non-autonomous non-Hermitian Hamiltonians, and in particular the PT symmetric Hamiltonians that gave rise to a new chapter of quantum mechanics, which deals with processes described by pseudoHermitian Hamiltonians by introducing a new metric operator.