Abstract
In these notes I should like to discuss some general features of a Hamiltonian quantum field theory, as well as to present some recent results regarding existence questions for certain model field theories. Especially exciting among these recent results are those pretaining to a rigorous Hamiltonian formulation of a relativistic scalar field with quartic self-interaction in a two-dimensional space time [1]. These promising results clearly make the study of model theories attractive, and their study as Hamiltonian theories especially so.
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