Quantum Mechanics from an Equivalence Principle
arXiv:hep-th/9705108 · doi:10.1016/S0370-2693(99)00113-6
Abstract
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the Hamilton-Jacobi equation which in turn implies the Schroedinger equation. In this context the Planck constant plays the role of covariantizing parameter. The construction is deeply related to the GL(2,C)-symmetry of the second-order differential equation associated to the Legendre transformation which selects, in the case of the quantum analogue of the Hamiltonian characteristic function, self-dual states which guarantee its existence for any physical system. The universal nature of the self-dual states implies the Schroedinger equation in any dimension.
1+10 pages. Standard Latex. Expanded version, references added, to appear in Phys. Lett. B
References in corpus (2)
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