arXiv:hep-th/0509207 · Modern Physics Letters A

SCALING OF VARIABLES AND THE RELATION BETWEEN NONCOMMUTATIVE PARAMETERS IN NONCOMMUTATIVE QUANTUM MECHANICS

O. BERTOLAMI, J. G. ROSA, C. M. L. DE ARAGÃO, P. Castorina, D. ZAPPALÀ

Published Mar 28, 2006• 93 citations

Abstract

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.

DOI: 10.1142/s0217732306019840

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News and views

AAPPS

The article gives an introductory summary of our recent results from the perspective of the new conceptual notion of noncommutative values of quantum observables, where basic quantum mechanics is seen a theory of particle dynamics that is intrinsically noncommutative.Real numbers as an algebra is really an abstract mathematical model for the description of values of physical quantities.Quantum mechanics illustrates the limitation of that perspective.The noncommutative values preserve the algebraic relations among the observables in their values.Such a value contains the complete information the theory presents for an observable on a given state.All physical quantities, including coordinates of the physical space for describing the location of a particle take definite noncommutative values.

AAPPS bulletinFeb 8, 20220 citations