Quantum Mechanics from an Equivalence Principle

Details Quantum Mechanics from an Equivalence Principle Quantum Mechanics from an Equivalence Principle

1997-05-15

arxiv.org/abs/hep-th/9705108v2

Phys.Lett. B450 (1999) 34-40

Physics

High Energy Physics

High Energy Physics - Theory

1+10 pages. Standard Latex. Expanded version, references added, to appear in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(99)00113-6

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.

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