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We formulate the time-dependent Ginzburg-Landau theory, with the assumptionof local equilibrium made in the reference frame floating with normalelectrons. This theory with floating nucleation kernel is applied to the farinfrared (FIR) conductivity in the Abrikosov vortex lattice. It yields betteragreement with recent experimental data [PRB {\bf 79}, 174525 (2009)] than thecustomary time-dependent Ginzburg-Landau theory.

Time-dependent Ginzburg-Landau theory with floating nucleation kernel; FIR conductivity in the Abrikosov vortex lattice