  This paper discusses the quantum mechanics of closed timelike curves (CTC)
and of other potential methods for time travel. We analyze a specific proposal
for such quantum time travel, the quantum description of CTCs based on
post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to
previously proposed quantum theories of time travel: the theory is physically
inequivalent to Deutsch's theory of CTCs, but it is consistent with
path-integral approaches (which are the best suited for analyzing quantum field
theory in curved spacetime). We derive the dynamical equations that a
chronology-respecting system interacting with a CTC will experience. We discuss
the possibility of time travel in the absence of general relativistic closed
timelike curves, and investigate the implications of P-CTCs for enhancing the
power of computation.
