Charge (physics) - Examples

Examples

Various charge quantum numbers have been introduced by theories of particle physics. These include the charges of the Standard Model:

• The color charge of quarks. The color charge generates the SU(3) color symmetry of quantum chromodynamics.
• The weak isospin quantum numbers of the electroweak interaction. It generates the SU(2) part of the electroweak SU(2) × U(1) symmetry. Weak isospin is a local symmetry, whose gauge bosons are the W and Z bosons.
• The electric charge for electromagnetic interactions.

Charges of approximate symmetries:

• The strong isospin charges. The symmetry groups is SU(2) flavor symmetry; the gauge bosons are the pions. The pions are not fundamental particles, and the symmetry is only approximate. It is a special case of flavor symmetry.
• Particle flavor charges, such as strangeness or charm. These generate the global SU(6) flavor symmetry of the fundamental particles; this symmetry is badly broken by the masses of the heavy quarks.

Hypothetical charges of extensions to the Standard Model:

• The magnetic charge, another charge in the theory of electromagnetism. Magnetic charges are not seen experimentally in laboratory experiments, but would be present for theories including magnetic monopoles.

In the formalism of particle theories charge-like quantum numbers can sometimes be inverted by means of a charge conjugation operator called C. Chiral fermions often cannot. Charge conjugation simply means that a given symmetry group occurs in two inequivalent (but still isomorphic) group representations. It is usually the case that the two charge-conjugate representations are fundamental representations of the Lie group. Their product then forms the adjoint representation of the group.

Thus, a common example is that the product of two charge-conjugate fundamental representations of SL(2,C) (the spinors) forms the adjoint rep of the Lorentz group SO(3,1); abstractly, one writes