Symmetry appears to be an important notion in physics. In this talk we address this concept through a new regard, and in particular some well known notions introduced in L3 are revisited. Thus, it is shown that Quantum Mechanics leads naturally to the mathematical structure underlying the description of symmetries in physics, namely Lie algebras and Lie groups. The distinction and relationship between these two structures is given using easy arguments. Moreover, a critical regard highlights an apparent confusion between real and complex numbers which in turn seems to be often present in the physical literature. A special attention is given to elucidate this apparent contradiction.
Time permitting, an explicit algorithm (which can be generalised in an easy manner to most of the Lie groups) is given to study the Lie group SU(3). In particular, it is show by mean of a differential realisation of su(3) (the Lie algebra associated to SU(3)) and without any more advance notions, how all unitary representations can be explicitly obtained in terms of polynomials.
