Real non-Archimedean structure of spacetime

A study is made of the process of measurement by means of $m$-adic (and, in particular, $p$-adic) numbers. It is shown that $m$-adic variables can be interpreted as variables that are infinite!y large compared with the unit of measurement. Morita's F function is used to construct a Bargmann–Fock representation for a non-Archimedean harmonic oscillator with infinitely high energies. A gauge connection between the real geometry of Minkowski spacetime $M_4$ and non-Archimedean geometry of the microscopic world is considered. Groups of non-Archimedean symmetries are realized as internal symmetries. The concept of a real non-Archimedean manifold is introduced. A group of conformal transformations associated with a Galois group is constructed.