  We present a complete solution of the soft x-ray edge problem within a
field-theoretic approach based on the Wiener-Hopf infinite-time technique. We
derive for the first time within this approach critical asymptotics of all the
relevant quantities for the x-ray problem as well as their nonuniversal
prefactors. Thereby we obtain the most complete field-theoretic solution of the
problem with a number of new experimentally relevant results. We make thorough
comparison of the proposed Wiener-Hopf technique with other approaches based on
finite-time methods. It is proven that the Fredholm, finite-time solution
converges smoothly to the Wiener-Hopf one and that the latter is stable with
respect to perturbations in the long-time limit. Further on we disclose a wide
interval of intermediate times showing quasicritical behavior deviating from
the Wiener-Hopf one. The quasicritical behavior of the core-hole Green function
is derived exactly from the Wiener-Hopf solution and the quasicritical exponent
is shown to match the result of Nozi\`eres and De Dominicis. The reasons for
the quasicritical behavior and the way of a crossover to the infinite-time
solution are expounded and the physical relevance of the Nozi\`eres and De
Dominicis as well as of the Winer-Hopf results are discussed.
