  Abstract interior-boundary conditions (IBC's) 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. The method was recently
applied to models where nonrelativistic scalar particles are linearly coupled
to a quantised field, the best known of which is the Nelson model. Since this
approach avoids the use of ultraviolet-cutoffs, there is no need for a
renormalisation procedure. Here, we extend the IBC method to pseudorelativistic
scalar particles that interact with a real bosonic field. We construct the
Hamiltonians for such models via abstract boundary conditions, describing their
action explicitly. In addition, we obtain a detailed characterisation of their
domain and make the connection to renormalisation techniques. As an example, we
apply the method to two relativistic variants of Nelson's model, which have
been renormalised for the first time by J. P. Eckmann and A. D. Sloan in 1970
and 1974, respectively.
