  We performed a time-resolved spectral analysis of 53 bright gamma-ray bursts
(GRBs) observed by \textit{Fermi}/GBM. Our sample consists of 908 individual
spectra extracted from the finest time slices in each GRB. We fitted them with
the synchrotron radiation model by considering the electron distributions in
five different cases: mono-energetic, single power-law, Maxwellian, traditional
fast cooling, and broken power-law. Our results were further qualified through
Bayesian Information Criterion (BIC) by comparing with the fit by empirical
models, namely the so-called Band function and cut-off power-law models. Our
study showed that the synchrotron models, except for the fast-cooling case, can
successfully fit most observed spectra, with the single power-law case being
the most preferred. We also found that the electron distribution indices for
the single power-law synchrotron fit in more than half of our spectra exhibits
flux-tracking behavior, i.e., the index increases/decreases with the flux
increasing/decreasing, implying that the distribution of the radiating
electrons is increasingly narrower with time before the flux peaks and becomes
more spreading afterward. Our results indicate that the synchrotron radiation
is still feasible as a radiation mechanism of the GRB prompt emission phase.
