The investigation of gauge transformations in the SLq(2) gauge field and thermodynamics model

Some problems about global transformations in the SLq(2) gauge field and co rrelative thermodynamics model have been investigated in this paper. We pro ved that the quantum trace of gauge potential is not gauge-invariant if we compose two GLq(2) gauge transformations. in addition, it has been discover ed in SLq(2) thermodynamics model that thermodynamics average of an observa ble quantity does not satisfy similar gauge invariance. We also found that the thermodynamics average can be only calculated in the case of zero energ y gap. This fact shows that the q-deformed energy equation in superconducti vity theory is unable to derive naturally from quantum trace model.