%0 Journal Article
%T Quantum Mechanics of a Quasi-Euclidean Space with Planck Length, Rotational Symmetry and Translational Symmetry
%A Yan Zhou
%A Junyan Zhang
%A Ernst Meyer
%A Xingkai Zhang
%A Jing Zhang
%J Journal of Applied Mathematics and Physics
%P 302-326
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.131014
%X This work is focused on a quasi-Euclidean space with UV cutoff, IR cutoff and symmetries. Mathematical analysis reveals that the UV cutoff results in the minimum structures of space. Dominated by rotational symmetry, the structure should be a local one <i>in situ</i> or on a sphere. Investigations show that a 10D minimum structure is a non-local one with transformability between in-situ state and spherical state due to its special topology. Based on the quantum behaviors of the 10D structure controlled by translational symmetry, IR cutoff determines two long-range interactions with dimensionless constants of ~1/137.036 and ~1/1.628E+38, respectively.
%K Planck Length
%K IR Cutoff
%K Symmetry
%K Fine Structure Constant (FSC)
%K Quantum Gravity
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140206