Speaker
Summary
We show that the cosmological constant $\Lambda$ can be considered as a new fundamental constant controlling the smallness of nonassociative effects in physics. We show that in this case there exists a minimal 4D scalar curvature (a unique Lorentz invariant quantity having the dimensions cm$^{-2}$): $R_{min} \approx \Lambda$. It immediately leads to a very simple explanation for the acceleration of the present Universe: the Universe reaches the minimally possible curvature and has to stay in this state.
Small nonassociative corrections for the SUSY operators $Q_{a, \dot a}$ are considered. The smallness is controlled by the ratio of the Planck length and a characteristic length $\ell_0 = \Lambda^{-1/2}$. Corresponding corrections of the momentum operator arising from the anticommutator of the SUSY operators are considered. The momentum operator corrections are defined via the anticommutator of the unperturbed SUSY operators $Q_{a, \dot a}$
and nonassociative corrections $Q_{1, a, \dot a}$. Choosing different anticommutators, one can obtain either a modified or $q$ -- deformed commutator of position $x^\mu$ and momentum operators $P_\nu$.
