Investigation of some formal aspects of the boson expansion technique in nuclear theory

The use of the boson expansion theory (BET) in nuclear physics now has about twenty years history, and a large number of papers is available in the literature. Some of them emphasize BET's practical use, successfully showing that it is in fact a very powerful, practical tool to understand the collective properties in nuclei. Others, on the other hand, concentrated more on formal aspects of the BET, and it is these formal aspects we deal with in this dissertation. The BET is not unique, and thus a variety of methods has been proposed. It was felt that it was desirable to see whether they were in fact different theories, or the difference was only apparent. Actually, at the surface, many theories look different from each other, having various merits and demerits. However, it is possible that they are more closely related than they appear; and, if so, it may be attempted to unify them in such a way that a new BET can be constructed which embodies all the merits of the various theories that have been known so far. With this goal in mind, every detailed comparison of two methods was explored: the commutator method (CM) and the Marumori-Yamamura-Tokunaga (MYT) method, which have been discussed most popularly in the past, though often with controversy. It was found that they are, in fact, equivalent theories if looked at from a particular point of view, although they are not necessarily exactly the same in every aspect. Similar comparison was also made with the generalized Holstein-Primakoff (GHP) and the Dyson methods