Symplectic Reduction and Poisson Geometry
Published in Penn State Archive, 2021
In the last hundred years, Classical Mechanics has been dwarfed by the development of Relativity and Quantum Mechanics. However, significant mathematical developments have been made to Classical Mechanics in the same time frame and this essay aims to explore some of the recent advances. The purpose of this essay is to understand Hamiltonian dynamics, Noether’s theorem and symmetry in a geometric framework using Poisson geometry. In particular, we want to analyse the case when the natural configuration space of a system is a Lie group G and transformations on the space correspond to the Lie group acting on itself.
Recommended citation: O'Callaghan, M. (2021). "Symplectic Reduction and Poisson Geometry." Preprint Pen Phill.
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