  General relativity allows solutions exhibiting closed timelike curves. Time
travel generates paradoxes and quantum mechanics generalizations were proposed
to solve those paradoxes. The implications of self-consistent interactions on
acausal region of space-time are investigated. If the correspondence principle
is true, then all generalizations of quantum mechanics on acausal manifolds are
not renormalizable. Therefore quantum mechanics can only be defined on global
hyperbolic manifolds and all general relativity solutions exhibiting time
travel are unphysical.
