The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not contain C 00 functions with compact support. In spite of this defect the support concept of //-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory. § 1. Introduction
An exact equation for the bound state of nucleons in the static neutral scalar model is obtained by using the field equation for Heisenberg operator and the method of canonical transformaticn. The formulation of the eigenvalue problem is completed by the analyticity consideration. In particular, a boundary condition at -r=O ( -i-r being the "negative imaginary" relative time) turns out that the derivative of the "wave function" with respect to -r must be zero at -r=O. The abnormal wlutions exist in this case as well as in the ladder approximation, but there is difference in nature between them for the zero meson mass case. The appearance of abnormal solutions is mainly due to the structure of the fundamental equation itself. This is demonstrated by handling a first order equation for the static neutral scalar model and the Bethe-Salpeter equation for the Lee model, in both cases of which the abnormal solutions do not appear.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.