부산대학교 도서관

Summary: ``We use Dirac's method for the quantization of constrainedsystems in order to quantize a spatially flat Friedmann-Lemaître-Robertson-Walker spacetime in the context of $f (Q)$ cosmology.When the coincident gauge is considered, the resulting minisuperspacesystem possesses second class constraints. This distinguishes thequantization process from the typical Wheeler-DeWitt quantization,which is applied for cosmological models where only first classconstraints are present (e.g. for models in general relativity or in$f(R)$ gravity). We introduce the Dirac brackets, find appropriatecanonical coordinates and then apply the canonical quantizationprocedure. We perform this method both in vacuum and in the presence ofmatter: a minimally coupled scalar field and a perfect fluid with alinear equation of state. We demonstrate that the matter contentchanges significantly the quantization procedure, with the perfectfluid even requiring to put in use the theory of fractional quantummechanics in which the power of the momentum in the Hamiltonian isassociated with the fractal dimension of a Lévy flight. The resultsof this analysis can be applied in $f(T)$ teleparallel cosmology, since$f (Q)$ and $f(T)$ theories have the same degrees of freedom and samedynamical constraints in cosmological studies.''