On the existence of Weisskopf-Wigner type theories

Abstract

It is shown that certain features of the Weisskopf-Wigner theory of natural line width can be generalized for the construction of a systematic, mathematically and logically autonomous approximation scheme for treating the interaction of a bound electron with photons. This scheme is equipped with its own hierarchy of orders which are not ruled by powers of the coupling constant. Under very weak conditions on the bound electron all Weisskopf-Wigner theories of finite order exist as ordinary quantum theories on ordinary Hilbert spaces HI and have strictly unitary time evolution operators UI(t), t< infinity . This implies in particular that in such theories the interaction of any finite number of states of the Dirac hydrogen atom with any bounded number of photons can never lead to divergencies. If an infrared catastrophe is banned by a small photon mass mu >0, Weisskopf-Wigner type theories of the interaction of an 'm-level atom', m< infinity , with any unbounded number of photons also exist and have strictly unitary time evolution operators. Some examples of novel applications of Wiesskopf-Wigner type theories are given.