Gauge Field, Fermi-Bose Duality, Minimization Entropy Reduction and Degeneracy of Critical Temperatures

Abstract

A non-Abelian gauge field is introduced to maintain the gauge invariance for the self-similar transformation, resulting in three conservation laws. It has been found that the non-Abelian gauge field is suitable to electromagnetic interaction. The Fermi-Bose duality for blocks makes blocks act as both fermi-blocks involving in spin interaction and non-spin interaction and bose-blocks carrying non-spin interaction. The self-similar transformation requires the block type inversion guaranteed by the gauge field. There is a constant and minimization entropy reduction in the transformation. It is realized that there is degeneracy of critical temperatures in the experiments for real materials. The thermodynamic dark parameters associated with the non-spin interaction should be taken seriously.