The uncharged particle named Higgs boson, with spin zero, is the quanta of a scalar field f defined as Higgs field, as well as the photon is the quanta of the electromagnetic field. It is assumed that the Higgs field acts like a continuous background medium even at short distances. It would play a fundamental role since it seems to represent the key to explain the origin of the mass of other elementary particles. The interaction of f with other fields is able to give mass to elementary particles. This quantum mechanism of mass creation is named generically the Higgs mechanism. The understanding of the Higgs mechanism is based on the “spontaneous symmetry breaking” and “gauge theory”.

The Higgs Mechanism, first invented by Peter Higgs, was used to lend mass to the gauge vector bosons of the weak interactions. The introduction of a complex scalar Higgs field into the Lagrangian, with a non-zero expectation value  turns the initially massless gauge bosons into massive bosons, while one of the two Higgs field components disappears.

In the present paper, we’ll discuss the Higgs mechanism, using  a one-dimensional and then a two-dimensional toy model, historically named the sigma model. The Higgs mechanism is generally described as a case of spontaneous symmetry breaking. Thus, the notion of spontaneous symmetry breaking (SSB) will be at the basis of this paper. The Higgs mechanism and his role in the Standard Model are also discussed.