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An experiment on the Weak Decay of Cobalt in 1956 showed that Parity Is Not A Symmetry of the universe. CHIRALITY A massless fermion is Left (Right) handed if the projection of its spin on the direction of motion of the particle has a positive (negative) value. (Projection zero is ruled out because the spin is half-integer.) The direction of spin is unaffected by a Lorentz boost along the direction of motion of the particle, and one can't boost to a frame where the particle moves in the opposite direction, because it moves at the speed of light. Therefore the sign of the projection is fixed for all reference frames. This fixed sign is called chirality. Chirality for a Dirac Field , ψ, is defined to be the Eigenvalue of γ5 . Any Dirac field can therefore be projected into its left or right handed component by the operation of (1±γ5)/2 on ψ. Both chiralities of a particle may appear in a theory. In this case the theory is called a vector theory. If only one chirality appears in a theory, then it is called a '''chiral theory'''. Quantum Chromodynamics is an example of a vector theory since both chiralities of all quarks appear in the theory. The Electroweak Theory is an example of a chiral theory, because only the left handed Neutrino appears in it (along with the right handed anti-neutrino). CHIRAL SYMMETRY Vector gauge theories with massless Dirac fermion fields exhibit chiral symmetry, ie, rotating the left handed and the right handed components independently makes no difference to the theory. We can write this as the action of rotation on the fields: : and or : and . With N flavors, we have unitary rotations instead: SU(N)L×SU(N)R. Massive fermions do not exhibit chiral symmetry. One also says that the mass term in the Lagrangian, breaks chiral symmetry explicitly. Spontaneous Chiral Symmetry Breaking may also occur in some theories, most notably in Quantum Chromodynamics . SEE ALSO
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