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Lecture
Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture covers canonical transformations, focusing on symplectic groups and their properties. It explains how to verify if a transformation is canonical, the role of real matrices, and the concept of preserved quantities. The lecture also delves into the symplectic group, exchange of coordinates and impulses, and the Jacobian matrix. It discusses the association between elements, multiplication properties, and the determinant of symplectic matrices. Additionally, it explores the concept of continuity in matrices and the identity matrix in phase space, emphasizing the preservation of quantities. The lecture concludes with a discussion on volumes in phase space and the canonical evolution of systems in statistical mechanics.