Poking at the Correspondence Principle with Derivative Couplings

It is shown that quantum mechanical systems obtained from a heuristic path integral quantization of lagrangians of the form $L= \sum_{n} \frac{1}{n!} f_n(q) \dot{q}^n$ violate in general the correspondence principle, unless $L$ is not more than quadratic in $\dot{q}$. The field theoretic counterpart of this result and its consequence on models of interacting scalar and vector fields and particularly the electroweak interactions, are briefly discussed.

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