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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 ...
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.
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.
These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to the maximum extent possible. The tree amplitudes in which all gauge bosons have the same helicity or all but one have the same helicity vanish. MHV amplitudes may be calculated very efficiently by means of the Parke–Taylor formula.
To see an in depth discussion of the two with examples, which also shows how chirality and helicity approach the same thing as speed approaches that of light, click the link entitled "Chirality and Helicity in Depth" on the same page. History of science: parity violation; Helicity, Chirality, Mass, and the Higgs (Quantum Diaries blog)
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.
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.
Magnetic helicity is a gauge-dependent quantity, because can be redefined by adding a gradient to it (gauge choosing).However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, [15] that is, independent of the gauge choice.