The subject of this talk will be about a physical achievements which were first
found mathematically and not by experiments : The ABEGHHK’tH mechanism (short
for Higgs mechanism). This mechanism is defined in the framework of gauge theory by
using the symmetry breaking. Thence, I will introduce gauge theory to give an idea of
what the Higgs mechanism describes.
Infinitesimal gauge transformations describe symmetries of the physical action and La-
grangian which are not only valid for a solution of the Euler-Lagrange equations. We are
going to define what an isotropy algebra is which is the essential component of symmetry
breaking and, thus, of the mass of gauge boson.