Phase Structure of Thermal QCD/QED:A Gauge Invariant Solution of the HTL Resummed Improved Ladder Dyson-Schwinger Equation

Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we propose a procedure how we can get the gauge invariant solution in the sense it satisfies the Ward-Takahashi identity. Results of the numerical analysis are shown and properties of the ``gauge-invariant'' solutions are discussed.