  We study fidelity decay by a uniform semiclassical approach, in the three
perturbation regimes, namely, the perturbative regime, the Fermi-golden-rule
(FGR) regime, and the Lyapunov regime.
  A semiclassical expression is derived for fidelity of initial Gaussian wave
packets with width of the order $\sqrt{\hbar}$
  ($\hbar$ being the effective Planck constant).
  Short time decay of fidelity of initial Gaussian wave packets is also
studied, with respect to two time scales introduced in the semiclassical
approach.
  In the perturbative regime, it is confirmed numerically that fidelity has the
FGR decay before the Gaussian decay sets in.
  An explanation is suggested to a non-FGR decay in the FGR regime, which has
been observed in a system with weak chaos in the classical limit, by using the
Levy distribution as an approximation for the distribution of action
difference.
  In the Lyapunov regime, it is shown that the average of the logarithm of
fidelity may have roughly the Lyapunov decay within some time interval, in
systems possessing large fluctuation of the finite-time Lyapunov exponent in
the classical limit.
