The present theory is based on the assumption that, at very small (Planck scale) distances our spacetime is discrete, and this discreteness influences the Planck scale physics. Considering our (3 + 1)-dimensional spacetime as a regular hypercubic lattice with a parameter a = λ_(Pl), where Pl is the Planck length, we have investigated a role of lattice artifact monopoles, which is essential near the Planck scale if the family-replicated gauge group model (FRGGM) is an extension of the Standard Model (SM) at high energies. It was shown that monopoles have N times smaller magnetic charge in the FRGGM than in the SM (N is the number of families in the FRGGM). These monopoles can give an additional contribution to functions of the renormalization-group equations for the running fine structure constants i(μ) (i = 1, 2, 3 correspond to the U(1), SU(2), and SU(3) gauge groups of the SM). We have used the Dirac relation for renormalized electric and magnetic charges. Also, we have estimated the enlargement of a n
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