  In spite of its problems with interactions, the first-quantized Klein-Gordon
equation is a satisfactory theory of free spinless particles. Moreover, the
usual theory may be extended to describe Lorentz-violating behavior, of the
same types that exist can in second-quantized scalar field theories. However,
because the construction of the theory requires a restriction to
positive-energy modes, the Hilbert space inner product and the position
operator depend explicitly on the form of the Lorentz violation.
