Monopoles Near the Planck Scale and Unification

Abstract

Considering our (3 + 1)-dimensional space-time as, in some way, discrete or lattice with a parameter a = λ P , where λ P is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants α i (µ) (i=1,2,3 correspond to the U(1), SU(2) and SU (3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have N f am times smaller magnetic charge in FRGGM than in SM (N f am is the number of families in FRGGM). We have estimated also the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at µ = µ G ∼ 10 18 GeV, we have the possibility of unification if the FRGGM-breakdown occurs at µ G ∼ 10 14 GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale µ GU T ≈ 10 18.4 GeV. We discussed the possibility of [SU (5)] 3 or [SO(10)] 3 (SUSY or not SUSY) unifications.

Theoretical and experimental status of magnetic monopoles

“…This is at odds with the modern understanding of renormalization as a continuous evolution of parameters, such as the charge, with change of energy scale. It would seem that this view of the renormalization group may be difficult to maintain without a perturbative framework: That is, at any energy scale Q, we might expect e(Q)g(Q) = n. (6.4) For this reason Laperashvili and Nielsen [125,126,127,128,129], following Zwanziger [80,82] argue that (6.4) holds at all scales, or in terms of the bare and renormalized quantization numbers, n = n 0 . That is, the electric and magnetic charges are renormalized by exactly inverse factors.…”

“…For this reason Laperashvili and co-workers [126][127][128][129][130], following Zwanziger [80,82], argue that (6.4) holds at all scales or in terms of the bare and renormalized quantization numbers, n = n 0 . That is, the electric and magnetic charges are renormalized by exactly inverse factors.…”

The Problem of Monopoles in the Standard and Family Replicated Models

“…The aim of the present talk is to show that monopoles cannot be seen in the Standard Model and in its usual extensions, known in the literature, up to the Planck scale [1,2]:…”

Theoretical and Experimental Status of Magnetic Monopoles

“…[This is (3.21) with A = A ′ given by the second form in (3.24) withn =ẑ.] Even though this is much more complicated than the Coulomb Hamiltonian, the wavefunction still may be separated: 127) where the radial and angular factors satisfy…”