SU(3) × SU(2) × U(1) Symmetries of Lattice System and Correspondence to Quantum Field Theory

Abstract

Three theorems on critical fluctuations and new concepts of isomorph spin, hyperspin, quablocks, and pioblocks are proposed, these new quantities correspond to the same symmetries although they have distinguishable values in different lattice systems. The self-similar transformations take place not only in the ordblocks, but also in the disblocks. In the quablocks sense, the critical fluctuation is analogous to the asymptotic freedom of the quark theory, and the reciprocal transformation between the ordblocks and disblocks is like the transfer between protons and neutrons. There are three transition temperatures, different temperature regions correspond to different symmetries and gauge invariances, leading to that there is no unified quantum theory.