Abstract
The Mandelstam representation is a statement about the region of analyticity and asymptotic behavior (polynomial boundedness) of a scattering amplitude. In virtue of the unitarity condition, however, these two are not completely independent. Some physical consequences, e.g., uniqueness, polynomial boundedness of the total cross section, etc., which have been already derived from the Mandelstam representation, are shown to be preserved, even if the polynomial boundedness is replaced by a somewhat weaker assumption. By making use of unitarity, analyticity, and crossing symmetry, the following type of scattering amplitude F = E + M, where E is an entire function in both variables s and t, while M denotes a Mandelstam-type function with finite number of subtraction, is shown to be ruled out. Similarly, F = EM is also ruled out, if one imposes the additional restriction that E should increase less fast than an exponential in one variable while the other is finite.
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