Hamiltonian Mechanics in 1+2 Dimensions
D. R. Grigore
TL;DR
This paper classifies all transitive symplectic manifolds under the Poincaré and Galilei groups in 1+2 dimensions, providing a comprehensive understanding of their geometric structures.
Contribution
It provides a complete classification of all transitive symplectic manifolds for these groups in 1+2 dimensions, filling a gap in geometric and mathematical physics.
Findings
List of all transitive symplectic manifolds identified
Classification results for Poincaré and Galilei groups
Implications for 1+2 dimensional physics and geometry
Abstract
A complete list of all transitive symplectic manifolds of the Poincar\'e and Galilei group in 1+2 dimensions is given.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Noncommutative and Quantum Gravity Theories · Nonlinear Waves and Solitons