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*SO*(3) — the group of rotations in three dimensions, whose elements are 3x3 orthogonal unimodular real matrices — is introduced and *SU*(2) is introduced as the universal covering group of *SO*(3). This chapter starts with a discussion of rotations in two dimensions, which should be familiar to everybody. Next, it is shown that the determinant of real orthogonal *n*x*n* matrices equals +1 or –1 and therefore the *O*(*n*) group consists of two disconnected pieces: rotations, for which the determinant equals +1 and reflections, for which the determinant equals –1. Since rotations are generated by angular momentum I identify the infinitesimal generators of *SO*(*n*) with the Cartesian components of angular momentum in appropriate units. Explicit evaluation of the structure constants shows the *so*(3) and *su*(2) algebras are isomorphic. The corresponding groups are shown to be homomorphic, *SO*(3) being doubly connected, while *SU*(2) is the simply connected covering group.

*Keywords: *
orthogonal matrices;
rotations;
reflections;
connectivity;
universal covering group

*Chapter.*
*3003 words.*
*Illustrated.*

*Subjects: *
Mathematical and Statistical Physics

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