标题： 量子理论在近平衡的经典力学中的起源 显示英文标题

标题： Quantum theory from classical mechanics near equilibrium

摘要： 我们考虑由哈密顿量$H(p,q)$描述的经典理论，该哈密顿量在广义动量$p$和广义坐标$q$均为零的点具有非退化极小值。我们假设广义动量和广义坐标的平方和是一个运动常数。在这种情况下，在点$p=0, q=0$附近的哈密顿量的二次部分起主导作用。我们假定一个经典观察者只能观测到对应于二次哈密顿量的物理量，并表明在这种情况下，他应该得出量子理论的规律支配他的世界的结论。 显示英文摘要

摘要： We consider classical theories described by Hamiltonians $H(p,q)$ that have a non-degenerate minimum at the point where generalized momenta $p$ and generalized coordinates $q$ vanish. We assume that the sum of squares of generalized momenta and generalized coordinates is an integral of motion. In this situation, in the neighborhood of the point $p=0, q=0$ quadratic part of a Hamiltonian plays a dominant role. We suppose that a classical observer can observe only physical quantities corresponding to quadratic Hamiltonians and show that in this case, he should conclude that the laws of quantum theory govern his world.