EP Quantum Mechanics
Encyclopedia : E : EP : EPQ : EP Quantum Mechanics
In
physics,
EP quantum mechanics is a theory of motion of point particles, partly included in the framework of quantum trajectory representation theories of quantum mechanics, based upon an
equivalence postulate similar in content to the
equivalence principle of
general relativity, rather than on the traditional
Copenhagen interpretation of
quantum mechanics. The
equivalence postulate states that all one-particle systems can be connected by a non-degenerate coordinate transformation, more precisely by a map over the
cotangent bundle of the position manifold, so that there exists a quantum
action function [S(q)] transforms as a
scalar field. Here, the action is defined as
- [d S(q) = p_i(q) dq^i]
is the
canonical one-form. This property is the heart of the EP formulation of quantum mechanics. An immediate consequence of the EP is the removal of the rest frame. The theory is based on symmetry properties of
Schwarzian derivative and on the quantum stationary Hamilton-Jacobi equation (QSHJE), which is a
partial differential equation for the quantum action function [S(q)], the quantum version of the
Hamilton-Jacobi equations differing from the classical one for the presence of a quantum potential term
- [Q(q) = \frac\]
with [\] denoting the
Schwarzian derivative. The QSHJE can be demonstrated to imply the
Schrödinger equation with square-summability of the wave function, and thus quantization of energy, due to continuity conditions of the quantum potential, without any assumption on the probabilistic interpretation of the wave function. The theory, which is a work in progress, may or may not include probabilistic interpretation as a consequence OR a hidden variable description of trajectories.
References
- Alon E. Faraggi, M. Matone (2000) "The Equivalence Postulate of Quantum Mechanics", International Journal of Modern Physics A, Volume 15, Issue 13, pp. 1869-2017. arXiv [hep-th/9809127]
- G. Bertoldi, Alon E. Faraggi, M. Matone (2000) "Equivalence principle, higher dimensional Mobius group and the hidden antisymmetric tensor of Quantum Mechanics", Class. Quantum Grav. 17 (2000) 3965–4005. arXiv [hep-th/9909201]
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