TL;DR
This paper investigates the quantization of Regge links, revealing that timelike triangle areas have a discrete spectrum linked to the Planck scale, demonstrated through a simplified solvable model.
Contribution
It introduces a quantization scheme for Regge links showing discrete timelike triangle spectra, supported by an exactly solvable reduced model.
Findings
Timelike triangle areas have a discrete spectrum.
The spectrum scale is at the Planckian level.
The results are validated in a simplified model.
Abstract
In quantum Regge calculus areas of timelike triangles possess discrete spectrum. This is because bivectors of these triangles are variables canonically conjugate to orthogonal connection matrices varying in the compact group. (The scale of quantum of this spectrum is nothing but Plankian one). This is checked in simple exactly solvable model - dimensionally reduced in some way Regge calculus.
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