Ultraviolet dimensional reduction of spacetime with zero-point length

Abstract Among the many disparate approaches towards quantum gravity, reduction of spacetime dimension in ultraviolet regime is expected to be a common thread. The spectral defined context diffusion processes on manifold. We show that with zero-point length has 3.5 when characteristic time size length. (negatively) diverges for an even shorter time, thus preventing reliable physical interpretation deep regime. thermodynamic by realizing free energy $$F(\beta )$$ F ( β ) field or ideal gas at finite temperature ( $$\beta ^{-1}$$ - 1 ) D dimensions scales as $$F\sim \beta ^{-D}$$ ∼ D . Using Schwinger’s proper formalism, we incorporating length, reduces 1.5 near Planck scale and then 1 This signifies “phase-transition” which (massless) bosonic four essentially behaves like radiation $$w=1/3$$ w = / 3 low energies, whereas scale, it equivalently having equation state parameter $$w=2$$ 2 Furthermore, can deduced from potential $$V_D(r)$$ V r interaction between two point-like sources separated distance r its scaling depends Comparing behavior conventional Yukawa-like potentials short distances, appears either 2 3 depending use massive massless force carriers probes.