Quantized massive-collective gauge fields and anomalous properties in high-$$T_\mathrm{c}$$ cuprates

Quantized massive gauge fields, which might mediate Cooper pair formation, have been presented as collective modes, which contain effects of spin fluctuation, charge fluctuation, and phonon, around doped holes from the viewpoint of adjacent interactions. Taking into account the restoration of spontaneous symmetry breaking, we have discussed the anomalous properties in the strange metal phase and the quantum criticality in high-\(T_\mathrm{c}\) cuprates. The present theoretical-formula satisfies both renormalization and unitalization conditions.