Generalized metric phase space for quantum systems and the uncertainty principle

C.M. Sarris and A.N. Proto

Physica A: Statistical Mechanics and its Applications, 2007, vol. 377, issue 1, 33-42

Abstract: We demonstrate that when the Gibbs entropy is an invariant of motion, following Information Theory procedures it is possible to define a generalized metric phase space for the temporal evolution of the mean values of a given Hamiltonian. The metric is positive definite and this fact leads to a metric tensor, K(t), whose properties are well defined. Working with these properties we shown that: (a) the Generalized Uncertainty Principle (GUP), is always the summation over the principal minors of order 2 belonging to K(t); (b) several invariants of motion can be derived from the metric tensor; and (c) particularly, under certain conditions, the GUP itself, is also a motion invariant.

Keywords: Quantum dynamics; Invariants of motion; Lie algebras (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:377:y:2007:i:1:p:33-42

DOI: 10.1016/j.physa.2006.10.093

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