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Prof. dr. S. Bentvelsen (UvA / NIKHEF) explains Quantum Physics
to the people in the Vondelpark in Amsterdam:

This is a lecture on Abelian Gauge symmetry of Lagrangians. In the first part I indicate how the global U(1) invariance of the Dirac Lagrangian leads to the conservation of electric charge. Then the global invariance is replaced by a local Gauge invariance, and covariant derivatives are introduced to restore the symmetry. In this way the Lagrangian of Quantum Electro Dynamics is derived, leading to the coupling of photons to the fermion fields. In the last part the Higgs potential is introduced for this U(1) invariance, where spontaneous symmetry breaking leads to a mass term of the vector field (i.e. the foton), and a resulting Higgs particle. In the Standard Model this mechanism gives rise to the masses of the W and Z bosons. It is an open question if this Higgs particle exists.

See also: Higgs boson found and Wikipedia.