On a direct description of pseudorelativistic Nelson Hamiltonians

Abstract

Abstract interior-boundary conditions allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in quantum field theory. This method, which comes without the need for renormalization, was recently applied to the nonrelativistic Nelson model. Here, we demonstrate the flexibility of the novel approach by applying it to two relativistic variants of Nelson’s model. The existence of Hamiltonians for these models was shown using renormalization techniques by Eckmann [Commun. Math. Phys. 18, 247 (1970); J. Math. Phys. 15, 190 (1974)]. However, many important properties, such as the domain and the action of the Hamiltonian, were not known. We construct the Hamiltonians for such models via abstract boundary conditions, describing their action explicitly for the first time. In addition, we obtain a detailed characterization of their domain.