truly nontrivial, 3+1-dimensional example of a relativistically invariant field theory has not yet been achieved.

There are, however, unresolved issues at a much earlier stage of QED that hark back to black-body radiation, the simplest and historically first problem involving the interaction of matter with radiation. The conceptual problems stemming from black-body radiation were partly resolved by quantum mechanics, i.e., by the the non-relativistic Schrödinger equation, which is, undoubtedly, one of the most successful of theories, for it describes matter at low energies almost completely. It is mathematically consistent and there are techniques available to compute relevant quantities. Moreover, it allows us to explain certain facts about bulk matter such as its stability, it extensivity, and the existence of thermodynamic functions. What has not been as successful, so far, is the incorporation of radiation phenomena, the very problem quantum mechanics set out to explain.

It ought to be possible to find a mathematically consistent theory, free of infinities, that describes the interaction of non-relativistic matter with radiation at moderate energies, such as atomic binding energies. It should not be necessary, as some physicists believe, to embed QED as a low energy part of a consistent high energy theory.

From such 