ABSTRACT
This chapter discusses unitary symmetry in the group theory in particle, nuclear, and Hadron physics by using simple examples from physics and mathematics. Lie groups are infinite groups which exhibit an additional property of their multiplication laws being differentiable. One observes that the differentiation merges well within the structure of a manifold. One can actually prove that there is a one-to-one correspondence between a Lie algebra and a simple connected Lie group. If it emerges that two different groups happen to have the same Lie algebra (i.e., their Lie algebrae are isomorphic) then clearly there has to be a one-to-one correspondence between the two groups – at least in the neighbourhood of each element. The chapter examines rotation of a two-dimensional vector and three-dimensional vector. It is shown that the collection of rotations in two dimensions is an Abelian group. But, rotations in three dimensions form a non-Abelian group.
