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

# symmetry group

# 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

# Strong Interactions and quarks

Quantum chromodynamics (QCD) is the gauge theory describing strong interactions between quarks. It constitutes a fundamental theory within the Standard Model and it is responsible for the portion. Weak and electromagnetic interactions are considered unified in the single symmetry group where , the weak hypercharge, is the generator of the group that is given by … Continue reading Strong Interactions and quarks