Quantization of Systems with Quadratic Derivative Interactions

We consider fields described by Lagrangian densities of the form ${\partial }^{\mu }\varphi G{\partial }_{\mu }\varphi$. We find that there is an ordering of operators in such systems which defines a unique Hamiltonian for which consistency between the Euler-Lagrange and Heisenberg field equations is obtained. This ordering results in a subtraction term which removes a divergent mass-like term to first order in the one-pion-to-one-pion transition amplitude.