Abstract
We construct several bounds on renormalization constants and on the asymptotic behavior of propagation functions and vertices. The inputs are experimental measurements and/or analyticity properties of vertex functions. We also discuss the connection between zeros in propagators, poles in vertex functions, and the values of coupling constants. This is the problem studied by Geshkenbein and Ioffe and by Meiman, and we discuss the possible physical significance of such zeros in terms of an extended Lee model. In particular we argue on the basis of this model and the scattering amplitude derived from it that there is no reason to exclude the existence of zeros in the propagator. This negates the arguments given for bounding the coupling constants in field theory.
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