  This work addresses the quantization of a self-interacting higher order time
derivative theory using path integrals. To quantize this system and avoid the
problems of energy not bounded from below and states of negative norm, we
observe the following steps: 1) We extend the theory to the complex plane and
in this sense we double the degrees of freedom. 2) We add a total derivative to
fix the convenient boundary conditions. 3) We check that the complex structure
is consistent. 4) To map from the complex space to the real space we introduce
reality conditions as second class constraints and we check that the
interactions do not generate more constraints. 5) We built the measure of the
complex path integral and we show that including currents the theory is
projected to a self-interacting real theory that is renormalizable.
