  In this paper, we develop a non-perturbation theory for describing
decoherence dynamics of electron charges in a double quantum dot gated by
electrodes. We extend the Feynman-Vernon influence functional theory to
fermionic environments and derive an exact master equation for the reduced
density matrix of electrons in the double dot for a general spectral density at
arbitrary temperature and bias. We then investigate the decoherence dynamics of
the double dot charge qubit with back-action of the reservoirs being fully
taken into account. Time-dependent fluctuations and leakage effects induced
from the dot-reservoir coupling are explicitly explored. The charge qubit
dynamics from the Markovian to non-Markovian regime is systematically studied
under various manipulating conditions. The decay behavior of charge qubit
coherence and the corresponding relaxation time $T_1$ and dephasing time $T_2$
are analyzed in details.
