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首页> 外文期刊>Journal of Physics Communications >From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics
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From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics

机译：从物理假设到经典和量子哈密顿和拉格朗日粒子力学

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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 dynamics of its infinitesimal parts--will give us a classical Hamiltonian system. Assuming the system is irreducible--specifying the state and the dynamics of the whole system tells us nothing about the state and the dynamics of its substructure--will give us a quantum Hamiltonian system. Assuming kinematic equivalence, that studying trajectories is equivalent to studying state evolution, will give us Lagrangian mechanics and limit the form of the Hamiltonian/Lagrangian to the one with scalar and vector potential forces.
机译：这项工作的目的是表明可以从几个简单的物理假设中得出经典和量子，哈密顿和拉格朗日的粒子力学。假设确定性和可逆的时间演化将为我们提供一个动力系统，该动力系统的状态集形成一个拓扑空间，并且其演化规律是自同胚的。假设系统是无限可简化的-指定状态和整个系统的动力学等效于给出状态及其无限小部分的动力学-将为我们提供经典的汉密尔顿系统。假设系统是不可约的-指定状态和整个系统的动力学不会告诉我们关于状态及其子结构的动力学-将会给我们一个量子哈密顿量系统。假设运动学等价性，研究轨迹等同于研究状态演化，将为我们提供拉格朗日力学，并将哈密顿/拉格朗日的形式限制为具有标量和矢量势力的形式。

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