Nonlinear Phenomena in Complex Systems, 2023, Vol.26, No.1, pp.27

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2023, Vol.26, No.1, pp.27 - 40

Discrete Quantum Gravity and Its Transition in Continuous Form in Nonperturbative Regime

Alexander Shalyt-Margolin

This paper presents an approach, independent of the space-time background, to gravitational studies in the discrete (lattice) form enabling one to express all fundamental quantities and their variations in terms of the present momenta in the case when a theory involves the maximal momentum (energy) P_max, E_max. The approach, in the explicit form, is applied to the Regge Calculus. In this case at low energies (far from the maximal ones) E << E_max, the study covers interaction with matter fields as well as the lattice weak-field expansion and strong coupling expansion. It is demonstrated that in the latter case of the proposed pattern a theory involves no long-range order. It is shown that, almost without any changes, this approach may be extended to the case of Causal Dynamical Triangulations (CDT) and, quite naturally, to the high energies E ≈ E_max. As this takes place, a theory involves the correctly defined low-energy transition to discrete and to continuous-form gravity.

Key words: maximal energies, nonperturbative quantum gravity, Regge Calculus

DOI: https://doi.org/10.33581/1561-4085-2023-26-1-27-40

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