Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 3

Effective actions for Regge state-sum models of quantum gravity

Pages: 631 – 653



Aleksandar Miković (Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologias, Lisboa, Portugal; and Grupo de Fisica Matemática, Universidade de Lisboa, Portugal)


We study the semiclassical expansion of the effective action for a Regge state-sum model and its dependence on the choice of the path-integral measure and the spectrum of the edge lengths. If the positivity of the edge lengths is imposed in the effective action equation, we find that the semiclassical expansion is not possible for the power-law measures, while the exponential measures allow the semiclassical expansion. Furthermore, the exponential measures can generate the cosmological constant term in the effective action as a quantum correction, with a naturally small value of the cosmological constant. We also find that in the case of a discrete-length spectrum, the semiclassical expansion is allowed only if the spectrum gap is much smaller than the Planck length.

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