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Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow. Helicity is one of the four known integral invariants of the Euler equations; the other three are energy, momentum and angular momentum.
The chirality of a molecule that has a helical, propeller, or screw-shaped geometry is called helicity [5] or helical chirality. [6] [7] The screw axis or the D n, or C n principle symmetry axis is considered to be the axis of chirality. Some sources consider helical chirality to be a type of axial chirality, [7] and some do not.
In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given polypeptide; the Zimm–Bragg model differs by incorporating the ease of propagation (self-replication) with respect to nucleation.
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. By ...
In theoretical particle physics, maximally helicity violating amplitudes (MHV) are amplitudes with massless external gauge bosons, where gauge bosons have a particular helicity and the other two have the opposite helicity. These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to the maximum extent ...
Macroscopic examples of chirality are found in the plant kingdom, the animal kingdom and all other groups of organisms. A simple example is the coiling direction of any climber plant, which can grow to form either a left- or right-handed helix. In anatomy, chirality is found in the imperfect mirror image symmetry of many kinds of animal bodies.
The two-component helicity eigenstates satisfy ^ (^) = (^) where are the Pauli matrices, ^ is the direction of the fermion momentum, = depending on whether spin is pointing in the same direction as ^ or opposite.
It is also rotationally invariant, in that a rotation applied to the system leaves the helicity unchanged. Helicity, however, is not Lorentz invariant; under the action of a Lorentz boost, the helicity may change sign. Consider, for example, a baseball, pitched as a gyroball, so that its spin axis is aligned with the direction of the pitch. It ...