Symmetries of the QCD

An important feature of the QCD is the conspicuous amount of symmetries of its lagrangian. First and foremost, its lagrangian is invariant under local gauge transformations, i.e. one can redefine the quark fields indipendently at every point in the space-time, without changing the physical content of the theory. This determines a number of implications in … Continue reading Symmetries of the QCD

The Minimal Supersymmetric extension of the Standard Model (MSSM)

The starting point for the construction of the Lagrangian of a such model is the SUSY Lagrangian, where the gauge invariance with respect to the group of the SM, , has to be imposed. In the minimal hypothesis, each particle included in the SM possesses a unique superpartner, i.e. formally a superfield has to replace … Continue reading The Minimal Supersymmetric extension of the Standard Model (MSSM)

Supersymmetry

Supersymmetry (SUSY) is one of the most compelling possible extensions of the Standard Model of particle physics, and one of the most promising theory candidate for a new principle about Nature that could be discovered at high-energy colliders such as the . The hierarchy problem represents the only indicator of the energy scale in which … Continue reading Supersymmetry

The Higgs mechanism

The simplest way to implement the SSB in the electroweak theory is achieved by adding the Higgs field, a complex scalar isospin doublet with four degrees of freedom, Without affecting the gauge invariance, it is possible to add to the Lagrangian of the electroweak interaction (*) the term which indicates the SSB, with  and in the potential explicited … Continue reading The Higgs mechanism

So, what about the Standard Model?

It is now possible to state that the Standard Model is a gauge theory invariant under  symmetry group given by the direct product of the symmetry group of the strong interaction, , with that of electroweak interaction, which also contains the symmetry group of electromagnetic interaction . The general form involving these fields is where: indicate leptons … Continue reading So, what about the Standard Model?

Electromagnetic interactions

The electromagnetic interaction is described by a gauge theory headed by the symmetry group whose density of the Lagrangian can be written as: where is the electromagnetic field tensor and is the gauge covariant derivative, with indicating the covariant four-potential of the electromagnetic field, generated by the charge ; is the external field due to … Continue reading Electromagnetic interactions