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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.
Helicity is the projection (dot product) of a spin pseudovector onto the direction of momentum (a true vector). Pseudoscalar particles, i.e. particles with spin 0 and odd parity, that is, a particle with no intrinsic spin with wave function that changes sign under parity inversion. Examples are pseudoscalar mesons.
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.
Consider, for example, a baseball, pitched as a gyroball, so that its spin axis is aligned with the direction of the pitch. It will have one helicity with respect to the point of view of the players on the field, but would appear to have a flipped helicity in any frame moving faster than the ball.
Helicity may refer to: Helicity (fluid mechanics) , the extent to which corkscrew-like motion occurs Helicity (particle physics) , the projection of the spin onto the direction of momentum
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.
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 ...
This implies that the lepton must be emitted with spin in the direction of its linear momentum (i.e., also right-handed). If, however, leptons were massless, they would only interact with the pion in the left-handed form (because for massless particles helicity is the same as chirality) and this decay mode would be prohibited.