Relativistic temperature and Higgs-like coupling of thermodynamic interactions

The thermodynamic interaction at thermodynamic equilibrium in the free fermion gas is described in an alternative way by the coupling of particles with a scalar thermodynamic field that features self-interaction. This alternative coupling is similar to the Higgs coupling and is helpful in understanding the temperature transformation at thermodynamic equilibrium under the Lorentz boost. As this coupling is applied in the abelian interaction fermion gas, nothing nontrivial is obtained. However, an interesting thing happens in the nonabelian interaction fermion gas where the difference appears for the diagonal and off-diagonal intermediate bosons as the Higgs-like coupling is added.