# From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics

@article{Carcassi2017FromPA, title={From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics}, author={Gabriele Carcassi and Christine A. Aidala and David John Baker and Lydia Bieri}, journal={Journal of Physics Communications}, year={2017}, volume={2} }

The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a dynamical system whose set of states forms a topological space and whose law of evolution is a self-homeomorphism. Assuming the system is infinitesimally reducible—specifying the state and the dynamics of the whole system is equivalent to giving the state and the…

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