Some Remarks on the Normal Ordering of Lagrangians

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Abstract
We study the properties of normally ordered nonpolynomial perturbations of a harmonic oscillator. It is found that the asymptotic behavior of the normally ordered object is not as bad as anticipated in a traditional approach; rather, it has exactly the same behavior as the unordered perturbation. The same arguments also hold in the general field-theoretic case of nonpolynomial Lagrangians. Furthermore, we study a class of perturbations which are entire functions for which the correct operation of normal ordering is well defined and equivalent to the traditional approach. The normal-ordering operator can be generalized to the case of several fields and thereby one may obtain an explicit representation of the time-ordering operator.

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