S-Matrix Formalism, Charge Renormalization, and Definition of the Hamiltonian in a Simple Field-Theoretical Model

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Abstract
A field‐theoretical model (the relativistic version of the Lee model) is exhibited for which one can rigorously prove that the essential features of the S‐matrix formalism (in particular analyticity) hold, even for point coupling, and that all charge renormalizations are finite. It is also shown that, although the interaction‐picture description fails, the total Hamiltonian may still be defined as a symmetric operator and it governs the dynamics of the interaction. Finally, we point out that the usual pathologies which appear in the current (static) version of the model are not an intrinsic feature of the theory, but rather the result of too crude oversimplifications.