M.Sc Thesis
M.Sc Student Eyal Subag Contractions of SO(4) Representations Department of Physics Full Professor Mann Ady Full Professor Baruch Ehud Moshe

Abstract

Contraction of Lie groups is a formal way to define a "limit" of Lie groups. There are also contractions of Lie algebras and of the representations of both the Lie groups and the Lie algebras. The method of contraction is known for more than fifty years and has many uses. It is most applicable in cases where the physical system changes its symmetry in some kind of a continuous way. In this work, we define and give examples for contraction of Lie algebras, and discuss the issue of contraction of their  representations. We will present the case of contraction of the finite dimensional, irreducible representations of so(3) to infinite dimensional, irreducible representations of iso(2)  according to a procedure that İnönü and Wigner suggested and later on was generalized by Weimar-Woods  for representations of semisimple compact Lie algebras. We then describe the representation theory of the Lie algebras so(4) and iso(3). We will survey the known contraction of so(4) to iso(3). Then we will describe the contraction of the finite dimensional, irreducible representations of so(4) to  infinite dimensional, irreducible representations of iso(3). To the best of the author's knowledge the contraction of the finite dimensional, irreducible representations of so(4) to  infinite dimensional, irreducible representations of iso(3) does not appear in the published literature.