Mukubwa, AbelMakokha, John Wanjala2026-05-052026-05-052021-11-02Mukubwa, A. & Makokha, J. W. (2021). Gauge-Invariant Wigner Function Extended to High Temperature Superconductivity. Social Science Research Network, pp. 1-19 https://ssrn.com/abstract=3954763 or http://dx.doi.org/10.2139/ssrn. 3954763http://erepository.kibu.ac.ke/handle/123456789/11666Journal ArticleThe realization of gauge-invariant Wigner function (GIWF) has revolutionized studies on quantized and classical electromagnetic fields and has been adapted to a magnetostatic phenomenon in superconducting systems. We apply the quantum fluid moment hierarchy equations in solving the conservative moment equation of the gauge-invariant Wigner operator. The results show that the lower critical field (𝐻𝑐1), the vortex radius (𝑟0) and the penetration depth (𝜆) show dependence on Cooper pair excitation energy (𝐸𝑘).enWigner operatorWigner functionflow velocityvortex radiuspenetration depthlower critical fieldArticle