  Due to the Heisenberg uncertainty principle, various classical systems
differing only on the scale smaller than Planck's cell correspond to the same
quantum system. This fact is used to find a unique semiclassical representation
without the Van Vleck determinant, applicable to a large class of correlation
functions expressible as quantum fidelity. As in the Feynman path integral
formulation of quantum mechanics, all contributing trajectories have the same
amplitude: that is why it is denoted the ``dephasing representation.'' By
relating the present approach to the problem of existence of true trajectories
near numerically-computed chaotic trajectories, the approximation is made
rigorous for any system in which the shadowing theorem holds. Numerical
implementation only requires computing actions along the unperturbed
trajectories and not finding the shadowing trajectories. While semiclassical
linear-response theory was used before in quasi-integrable and chaotic systems,
here its validity is justified in the most generic, mixed systems. Dephasing
representation appears to be a rare practical method to calculate quantum
correlation functions in nonuniversal regimes in many-dimensional systems where
exact quantum calculations are impossible.
