Remarks on the Application of the Jost-Lehmann-Dyson Representation to Equal-Time Commutators

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Abstract
It is shown that Jost-Lehmann-Dyson spectral functions for matrix elements of scalar field commutators can lead to the existence of (finite) equal-time commutators with an arbitrary number of gradient terms. The conventional mechanism for the appearance of gradient terms is via the covariant tensor operators acting on the scalar commutator functions. These terms we call of "kinematical origin," whereas the first-mentioned purely scalar mechanism is called "nonkinematical." This latter possibility seems to have been overlooked in the recent literature.

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