A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality). "Mirror Image" is an episode of the Television series The Twilight Zone. In Geometry, a figure is chiral (and said to have chirality) if it is not identical to its Mirror image, or more particularly if it cannot be mapped to The spin of a particle may be used to define a handedness for that particle. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin A symmetry transformation between the two is called parity. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. The action of parity acting on a Dirac fermion is called chiral symmetry. In Particle physics, a Dirac fermion is a Fermion which is not its own Anti-particle.

An experiment on the weak decay of cobalt in 1956 showed that parity is not a symmetry of the universe. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature Cobalt (ˈkoʊbɒlt is a hard lustrous silver-grey Metal, a Chemical element with symbol Co. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate.

## Chirality and helicity

The helicity of a particle is Right-handed if the direction of its spin is the same as the direction of its motion. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin It is Left-handed if the directions of spin and motion are opposite. By convention for rotation, a standard clock, tossed with its face directed forwards, has Left-handed helicity. Circadian Locomotor Output Cycles Kaput, or Clock is a gene which encodes proteins regulating Circadian rhythm. Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: Left is negative, Right is positive. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product

The chirality of a particle is more abstract. It is determined by whether the particle transforms in a right or left handed representation of the Poincaré group. (However, some representations, such as Dirac spinors, have both right and left handed components. In cases like this, we can define projection operators that project out either the right or left hand components and discuss the right and left handed portions of the representation. )

For massless particles — such as the photon, the gluon, and the (hypothetical) graviton — chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework In Particle physics, helicity is the projection of the spin \vec S onto the direction of momentum \hat p: h = \vec

For particles that do have mass — such as electrons, quarks, and neutrinos — chirality and helicity must be distinguished. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost In the case of these particles, it is possible for an observer to change to a reference frame that overtakes the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as 'apparent chirality') will be reversed.

A massless particle moves with the speed of light, so a real observer (who must always travel at less than the speed of light) cannot be in any reference frame where the particle appears to reverse its relative direction, meaning that all real observers see the same chirality. Because of this, the direction of spin of massless particles is not affected by a Lorentz boost (change of viewpoint) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: the helicity is a relativistic invariant. In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to

With the discovery of neutrino oscillations, which imply that neutrinos have mass, the only observed massless particle is the photon. Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a Neutrino created with a specific Lepton Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The gluon also is expected to be massless, although the assumption that it is massless has not been tested. Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the Hence, these are the only two particles now known for which helicity could be identical to chirality, and only one that has been confirmed by measurement. All other observed particles have mass and thus may have different helicities in different reference frames. It is still possible that as-yet unobserved particles, like the graviton, might be massless, and hence have invariant helicity like the photon. In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena It is also not known for certain that the gluon is actually massless, it is only supposed; all that is certain from measurement is that if it is not zero then its mass must be very small. Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the Because of confinement, observation of gluons is complicated and difficult; it may be that they cannot exist as a free particle and only come in bound states called glueballs. Color confinement, often called just confinement, is the Physics phenomenon that Color charged particles (such as Quarks cannot be isolated singularly Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the In Physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object In Particle physics, a glueball is a strongly interacting particle containing no valence Quarks It is composed entirely of Gluons Such a state

## Chiral theories

It has been observed that only left-handed fermions interact with the weak interaction. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In most circumstances, two left-handed fermions interact more strongly than right-handed or opposite-handed fermions. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. Experiments sensitive to this effect imply that the universe has a preference for left-handed chirality, which violates a symmetry of the other forces of nature.

Chirality for a Dirac fermion ψ is defined by the operator γ5, which has eigenvalues ±1. In Quantum field theory, a fermionic field is a Quantum field whose quanta are Fermions that is they obey Fermi-Dirac statistics. In Mathematical physics, the gamma matrices, {γ0 γ1 γ2 γ3} also known as the Dirac matrices, form a matrix-valued In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes Any Dirac field can therefore be projected into its left- or right-handed component by the operation of the projection operator (1–γ5)/2 or (1+γ5)/2 acting on ψ. The coupling of the weak interaction to fermions is proportional to such a projection operator, which is responsible for its parity symmetry violation. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate.

A common source of confusion is due to conflating this operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that the chirality operator is equivalent to helicity for massless fields only, for which helicity is not frame-dependent. For massive particles, chirality is not the same as helicity so there is no frame dependence of the weak interaction: a particle that interacts with the weak force does so in every frame.

A theory that is asymmetric between chiralities is called a chiral theory, while a parity symmetric theory is sometimes called a vector theory. Most pieces of the Standard Model of physics are non-chiral, which may be due to problems of anomaly cancellation in chiral theories. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles In Quantum physics an anomaly or quantum anomaly is the failure of a Symmetry of a theory's classical action to be a symmetry of any regularization Quantum chromodynamics is an example of a vector theory since both chiralities of all quarks appear in the theory, and couple the same way. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the

The electroweak theory developed in the mid twentieth century is an example of a chiral theory. In Particle physics, the electroweak interaction is the unified description of two of the four Fundamental interactions of nature Electromagnetism and the The twentieth century of the Common Era began on Originally, it assumed that neutrinos were massless, and only assumed the existence of left-handed neutrinos (along with their complementary right-handed anti-neutrinos). Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost After the observation of neutrino oscillations, which imply that neutrinos are massive like all other fermions, the revised theories of the electroweak interaction now include both right- and left-handed neutrinos. Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a Neutrino created with a specific Lepton Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, the electroweak interaction is the unified description of two of the four Fundamental interactions of nature Electromagnetism and the Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost However, it is still a chiral theory, as it does not respect parity symmetry.

The exact nature of the neutrino is still unsettled and so the electroweak theories that have been proposed are different, but most accommodate the chirality of neutrinos in the same way as was already done for all other fermions. Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost In Particle physics, the electroweak interaction is the unified description of two of the four Fundamental interactions of nature Electromagnetism and the Neutrinos are Elementary particles that travel close to the Speed of light, lack an Electric charge, are able to pass through ordinary matter almost In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi.

## Chiral symmetry

Vector gauge theories with massless Dirac fermion fields ψ exhibit chiral symmetry, i. In Quantum field theory, chiral symmetry is a possible symmetry of the Lagrangian under which the left-handed and right-handed parts 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:

$\psi_L\rightarrow e^{i\theta_L}\psi_L$  and  $\psi_R\rightarrow \psi_R$

or

$\psi_L\rightarrow \psi_L$  and   $\psi_R\rightarrow e^{i\theta_R}\psi_R.$

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, $m\overline\psi\psi$ breaks chiral symmetry explicitly. Spontaneous chiral symmetry breaking may also occur in some theories, most notably in quantum chromodynamics. In Physics, spontaneous symmetry breaking occurs when a system that is symmetric with respect to some Symmetry group goes into a Vacuum state Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the