Chirality (physics) - Chiral Symmetry

Chiral Symmetry

Vector gauge theories with massless Dirac fermion fields exhibit chiral symmetry, i.e., 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.