A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity. The action of parity acting on a Dirac fermion is called chiral symmetry. // Geometry In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly cant be mapped to its mirror images by rotations and translations alone. ... In physics, a parity transformation (also called parity) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to -1, and hence cannot reduce to a rotation. ...

An experiment on the weak decay of cobalt in 1956 showed that parity is not a symmetry of the universe. The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... This article is on the periodic element. ... In physics, a parity transformation (also called parity) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to -1, and hence cannot reduce to a rotation. ...

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. The terms spin and SPIN have several meanings, including those primarily discussed as spinning: For spin in sub-atomic physics, see spin (physics) For the stalled aircraft maneuver or any of several forms of loss of control in aircraft, see spin (flight) For the periodical, see Spin Magazine For the...

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. In physics, a Dirac field is a fermionic field (usually a quantized field, as usual in quantum field theory) associated with spin 1/2 fermions such as the electron or muon. ...

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). Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... The neutrino is an elementary particle. ...

Chiral symmetry

Vector gauge theories with massless Dirac fermions (ψ) 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. Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ...

See also

• Spinors and Dirac fields
• Quantum chromodynamics
• Electroweak theory
• Chirality (disambiguation and short general information)

In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ... In physics, a Dirac field is a fermionic field (usually a quantized field, as usual in quantum field theory) associated with spin 1/2 fermions such as the electron or muon. ... Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... Chirality refers to several phenomena, all having to do with objects that differ from their mirror image. ...

References and external links

• History of science: parity violation