  Recently, a self-contained trajectory-based formulation of non-relativistic
quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4
(2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions
or complex amplitudes of any kind. Quantum states are represented as ensembles
of real-valued quantum trajectories that extremize a suitable action. Here, the
trajectory-based approach is developed into a viable, generally covariant,
relativistic quantum theory for single (spin-zero, massive) particles. Central
to this development is the introduction of a new notion of global simultaneity
for accelerated particles--together with basic postulates concerning
probability conservation and causality. The latter postulate is found to be
violated by the Klein-Gordon equation, leading to its well-known problems as a
single-particle theory. Various examples are considered, including the time
evolution of a relativistic Gaussian wavepacket.
