From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
- URL: http://arxiv.org/abs/2003.01070v1
- Date: Mon, 2 Mar 2020 18:01:34 GMT
- Title: From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
- Authors: P.V. Moniz and S. Jalalzadeh
- Abstract summary: This manuscript suggests the extension of fractional quantum mechanics to cosmological settings.
The application of fractional calculus in quantum cosmology is introduced.
An example of investigation is provided by means of a very simple model.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Fractional calculus is a couple of centuries old, but its development has
been less embraced and it was only within the last century that a program of
applications for physics started. Regarding quantum physics, it has been only
in the previous decade or so that the corresponding literature resulted in a
set of defying papers. In such a context, this manuscript constitutes a cordial
invitation, whose purpose is simply to suggest, mostly through a heuristic and
unpretentious presentation, the extension of fractional quantum mechanics to
cosmological settings. Being more specific, we start by outlining a historical
summary of fractional calculus. Then, following this motivation, a (very) brief
appraisal of fractional quantum mechanics is presented, but where details
(namely those of a mathematical nature) are left for literature perusing.
Subsequently, the application of fractional calculus in quantum cosmology is
introduced, advocating it as worthy to consider: if the progress of fractional
calculus serves as an argument, indeed useful consequences will also be drawn
(to cite from Leibnitz). In particular, we discuss different difficulties that
may affect the operational framework to employ, namely the issues of
minisuperspace covariance and fractional derivatives, for instance. An example
of investigation is provided by means of a very simple model. Concretely, we
restrict ourselves to speculate that with minimal fractional calculus elements,
we may have a peculiar tool to inspect the flatness problem of standard
cosmology. In summary, the subject of fractional quantum cosmology is herewith
proposed, merely realized in terms of an open program constituted by several
challenges.
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