Foldy-wouthuysen transformation and its generalisations

Abstract

The purpose of this thesis is to survey the developments in the field opened up in 1950 by Foldy and Wouthuysen. The investigations to be discussed here have all been concerned with the derivation of certain transformations (which are now all known as Foldy-Wouthuysen transformations, after the original workers); these transformations yield new (though, of course unitarily equivalent) representations of the conventional one-particle theories, which have a special property: the positive and negative energy states remain separate under the application of all the relevant operators of the theory.

The present survey is limited in several ways. Mo attempt has been made to include papers containing computational applications of the Foldy-Wouthuysen transformation; or papers which generalise the transformation to the case of field theory (of which there is only one, to the author’s knowledge). However, full references to these papers are given.

The order of development in the present work is not wholly historical. The thesis has been put into two parts, A and B. Part A deals with single-particle transformations, part B with two-particle transformations. This involved splitting a paper by Eriksen which deals with both cases by the same method.