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A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality).The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality.
In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign. The handedness in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear ...
An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
By contrast, for massive particles, distinct chirality states (e.g., as occur in the weak interaction charges) have both positive and negative helicity components, in ratios proportional to the mass of the particle. A treatment of the helicity of gravitational waves can be found in Weinberg. [5]
Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa. Two types of helix shown in comparison. This shows the two chiralities of helices. One is left-handed and the other is right-handed.
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.
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.
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.