Symmetries and their breaking in the fundamental laws of physics

Abstract: Symmetries in the Physical Laws of Nature lead to observable effects. Beyond regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetry requirement under exchange of identical fermions led to the colour degree of freedom, the charge for the interactions of quarks and gluons in the SU(3) local gauge symmetry. Parity Violation in weak interactions led to consider the Chiral Fields with definite transformation properties under the weak isospin gauge group of the ElectroWeak SU(2)xU(1) Symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-Reversal-Violation has been observed with Entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies leads to Quark-Lepton Symmetry. Neutrinos were postulated to save energy and angular momentum conservation in beta decay. The discovery of neutrino oscillations led to a new era about their origin of mass, mixing, discrete symmetries and the global lepton-number violation. Leptogenesis may be the source of the matter-antimatter asymmetry in the Universe. The discovery of quarks and leptons and the mediators of their interactions, with observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. Gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the Origin of Mass, without affecting the interactions: the Brout-Englert-Higgs Mechanism which produces the Higgs Boson as a remnant. Open present problems are addressed with the search of New Physics Beyond-the-Standard-Model.