Abstract
It is shown that the Lie algebra of globally Hamiltonian vector fields on a compact symplectic manifold can be lifted to a Lie algebra of smooth functions on the manifold under Poisson bracket. This implies that any algebra of symmetries of a classical mechanical system described by such a manifold may be realised as an algebra of observables (smooth functions). Parallels between lifting problems in classical and quantum mechanics are explored.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
