Symplectic reduction of classical mechanics on shape space

DOI10.1007/s10701-022-00613-6OpenAlexW4296998472WikidataQ126104979 ScholiaQ126104979MaRDI QIDQ2081065

Peter Pickl, Sahand Tokasi

Publication date: 12 October 2022

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.07041

zbMATH Keywords

symplectic formphase spacescale invariancesimilarity groupprinciple of relationalismreduced Hamiltonian form

Mathematics Subject Classification ID

Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Hamiltonian and Lagrangian mechanics (70H99) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10) Axiomatics, foundations (70A99)

Cites Work

• Reduction of symplectic manifolds with symmetry
• A universal phase space for particles in Yang-Mills fields
• Quantum motion on shape space and the gauge dependent emergence of dynamics and probability in absolute space and time
• The solution to the problem of time in shape dynamics
• Scale-invariant gravity: particle dynamics
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