Second Level Degree in Mathematics
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HAMILTONIAN MECHANICS - 6 CFU
From MATHEMATICAL PHYSICS (SECOND CYCLE DEGREE Physics)
Teacher
Paolo Rossi
Scheduled Period
I Year - 2 Semester | 02/03/2020 - 12/06/2020
Hours: 48 (48 lezione)
Prerequisites
Basics of algebra and differential geometry (the very basics of differential geometry will be recalled at the beginning of the course, if needed).
Basic knowledge of Hamiltonian mechanics and/or quantum mechanics would help putting the course content into context, but is not strictly needed.
Target skills and knowledge
By the end of the course the student should be able to navigate the technical literature on the subject and read and understand at least some of the research papers. He/She should acquire the skills necessary to solve problems by applying the notions and methods discussed in the course.
Examination methods
To be decided depending also on the number of students, but probably either a relatively simple written exam granting access to an oral exposition in the form of a short seminar plus some questions, or a written exam containing both simple exercises and questions on theory.
Assessment criteria
Evaluation will first focus on the student's acquisition of the course core material and then his/her ability to apply it to understand and possibly solve related problems.
Course contents
Hamiltonian systems in Poisson manifolds
(Poisson algebras, deformation theory, Poisson manifolds and their geometry,...).
Integrability
(reminder of Arnold-Liouville integrability, Lax representations, bihamiltonian structures,...).
Elements of quantization
(basic ideas of quantum mechanics, elements of deformation quantization, quantum mechanics in phase space,...).
Evolutionary Hamiltonian PDEs
(as infinite dimensional Hamiltonian systems, modern theory of integrable PDEs,...).
Planned learning activities and teaching methods
Lectures are given at the blackboard.
Additional notes about suggested reading
References will be given on the various topics, as the course progresses, but the lectures will be as self-contained as possible