  Starting from the Abelian Higgs field theory, we construct the theory of
quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space --
time dimensions in the limit of infinitely thin strings, the conformal anomaly
is absent, and the quantum theory exists. We also study an analogue of the
Aharonov--Bohm effect: the corresponding topological interaction is
proportional to the linking number of the string world sheet and the particle
world trajectory. The creation operators of the strings are explicitly
constructed in the path integral and in the Hamiltonian formulation of the
theory. We show that the Aharonov--Bohm effect gives rise to several nontrivial
commutation relations.
